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: