Balbharti 12th Maharashtra State Board Maths Solutions Book Pdf Chapter 3 Indefinite Integration Ex 3.4 Questions and Answers.
12th Maths Part 2 Indefinite Integration Exercise 3.4 Questions And Answers Maharashtra Board
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:
Class 12 Maharashtra State Board Maths Solution