# 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:

Question 2.
$$\frac{x^{2}}{\left(x^{2}+1\right)\left(x^{2}-2\right)\left(x^{2}+3\right)}$$
Solution:

Question 3.
$$\frac{12 x+3}{6 x^{2}+13 x-63}$$
Solution:

Question 4.
$$\frac{2 x}{4-3 x-x^{2}}$$
Solution:

Question 5.
$$\frac{x^{2}+x-1}{x^{2}+x-6}$$
Solution:

Question 6.
$$\frac{6 x^{3}+5 x^{2}-7}{3 x^{2}-2 x-1}$$
Solution:

Question 7.
$$\frac{12 x^{2}-2 x-9}{\left(4 x^{2}-1\right)(x+3)}$$
Solution:

Question 8.
$$\frac{1}{x\left(x^{5}+1\right)}$$
Solution:

Question 9.
$$\frac{2 x^{2}-1}{x^{4}+9 x^{2}+20}$$
Solution:

Question 10.
$$\frac{x^{2}+3}{\left(x^{2}-1\right)\left(x^{2}-2\right)}$$
Solution:

Question 11.
$$\frac{2 x}{\left(2+x^{2}\right)\left(3+x^{2}\right)}$$
Solution:

Question 12.
$$\frac{2^{x}}{4^{x}-3 \cdot 2^{x}-4}$$
Solution:

Question 13.
$$\frac{3 x-2}{(x+1)^{2}(x+3)}$$
Solution:

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

Question 15.
$$\frac{1}{x\left(1+4 x^{3}+3 x^{6}\right)}$$
Solution:

Question 16.
$$\frac{1}{x^{3}-1}$$
Solution:

Question 17.
$$\frac{(3 \sin x-2) \cdot \cos x}{5-4 \sin x-\cos ^{2} x}$$
Solution:

Question 18.
$$\frac{1}{\sin x+\sin 2 x}$$
Solution:

Question 19.
$$\frac{1}{2 \sin x+\sin 2 x}$$
Solution:

Question 20.
$$\frac{1}{\sin 2 x+\cos x}$$
Solution:

Question 21.
$$\frac{1}{\sin x \cdot(3+2 \cos x)}$$
Solution:

Question 22.
$$\frac{5 \cdot e^{x}}{\left(e^{x}+1\right)\left(e^{2 x}+9\right)}$$
Solution:

Question 23.
$$\frac{2 \log x+3}{x(3 \log x+2)\left[(\log x)^{2}+1\right]}$$
Solution: