Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4

   

Balbharti 12th Maharashtra State Board Maths Solutions Book Pdf Chapter 3 Indefinite Integration Ex 3.4 Questions and Answers.

Maharashtra State Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4

I. Integrate the following w. r. t. x:

Question 1.
\(\frac{x^{2}+2}{(x-1)(x+2)(x+3)}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q1
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q1.1

Question 2.
\(\frac{x^{2}}{\left(x^{2}+1\right)\left(x^{2}-2\right)\left(x^{2}+3\right)}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q2
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q2.1
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q2.2

Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4

Question 3.
\(\frac{12 x+3}{6 x^{2}+13 x-63}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q3
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q3.1

Question 4.
\(\frac{2 x}{4-3 x-x^{2}}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q4

Question 5.
\(\frac{x^{2}+x-1}{x^{2}+x-6}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q5
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q5.1

Question 6.
\(\frac{6 x^{3}+5 x^{2}-7}{3 x^{2}-2 x-1}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q6
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q6.1

Question 7.
\(\frac{12 x^{2}-2 x-9}{\left(4 x^{2}-1\right)(x+3)}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q7
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q7.1

Question 8.
\(\frac{1}{x\left(x^{5}+1\right)}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q8

Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4

Question 9.
\(\frac{2 x^{2}-1}{x^{4}+9 x^{2}+20}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q9
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q9.1
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q9.2

Question 10.
\(\frac{x^{2}+3}{\left(x^{2}-1\right)\left(x^{2}-2\right)}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q10
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q10.1
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q10.2

Question 11.
\(\frac{2 x}{\left(2+x^{2}\right)\left(3+x^{2}\right)}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q11

Question 12.
\(\frac{2^{x}}{4^{x}-3 \cdot 2^{x}-4}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q12
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q12.1

Question 13.
\(\frac{3 x-2}{(x+1)^{2}(x+3)}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q13
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q13.1

Question 14.
\(\frac{5 x^{2}+20 x+6}{x^{3}+2 x^{2}+x}\)
Solution:
Let I = ∫\(\frac{5 x^{2}+20 x+6}{x^{3}+2 x^{2}+x}\) dx
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q14
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q14.1

Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4

Question 15.
\(\frac{1}{x\left(1+4 x^{3}+3 x^{6}\right)}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q15
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q15.1
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q15.2

Question 16.
\(\frac{1}{x^{3}-1}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q16
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q16.1
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q16.2
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q16.3

Question 17.
\(\frac{(3 \sin x-2) \cdot \cos x}{5-4 \sin x-\cos ^{2} x}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q17
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q17.1
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q17.2

Question 18.
\(\frac{1}{\sin x+\sin 2 x}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q18
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q18.1
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q18.2

Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4

Question 19.
\(\frac{1}{2 \sin x+\sin 2 x}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q19
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q19.1
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q19.2
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q19.3

Question 20.
\(\frac{1}{\sin 2 x+\cos x}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q20
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q20.1
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q20.2

Question 21.
\(\frac{1}{\sin x \cdot(3+2 \cos x)}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q21
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q21.1
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q21.2

Question 22.
\(\frac{5 \cdot e^{x}}{\left(e^{x}+1\right)\left(e^{2 x}+9\right)}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q22
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q22.1

Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4

Question 23.
\(\frac{2 \log x+3}{x(3 \log x+2)\left[(\log x)^{2}+1\right]}\)
Solution:
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q23
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q23.1
Maharashtra Board 12th Maths Solutions Chapter 3 Indefinite Integration Ex 3.4 Q23.2

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