OP Malhotra Class 12 Maths Solutions Chapter 14 Indefinite Integral-2 Ex 14(c)

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S Chand Class 12 ICSE Maths Solutions Chapter 14 Indefinite Integral-2 Ex 14(c)

Question 1.
\(\int x \sin 2 x d x\)
Solution:

Question 2.
\(\int x \sec ^2 x d x\)
Solution:

Question 3.
\(\int x^2 e^x d x\)
Solution:

Question 4.
\(\int x \cos 2 x d x\)
Solution:

Question 5.
\(\int(1+x) \cos 2 x d x\)
Solution:

Question 6.
\(\int\left(1-x^2\right) \log x d x\)
Solution:

Question 7.
\(\int x^2 \sin x d x\)
Solution:

Question 8.
\(\int(\log x)^2 d x\)
Solution:

Question 9.
\(\int 2 x e^{5 x} d x\)
Solution:

Question 10.
\(\int \frac{\log \left(1+x^2\right)}{x^2} d x\)
Solution:

Question 11.
\(\int x^2 \log x d x\)
Solution:

Question 12.
\(\int x^3 \log _e x^2 d x\)
Solution:

Question 13.
\(\int x \sin ^2 3 x d x\)
Solution:

Question 14.
\(\int \frac{x-\sin x}{1-\cos x} d x\)
Solution:

Question 15.
\(\int \cos ^{-1} x d x\)
Solution:

Question 16.
\(\int \cot ^{-1} x d x\)
Solution:

Question 17.

Question 18.
\(\int x^2 \cos ^{-1} x d x\)
Solution:

Question 19.
\(\int \sin \sqrt{x} d x\)
Solution:

Question 20.
\(\int \tan ^{-1} \sqrt{x} d x\)
Solution:

Question 21.
\(\int \frac{\log x}{x^2} d x\)
Solution:

Question 22.
\(\int x \sin ^{-1} x d x\)
Solution:

Question 23.
\(\int \frac{\log (\log x)}{x} d x\)
Solution:

Question 24.
\(\int \sin ^3 \sqrt{x} d x\)
Solution:

Question 25.

Question 26.
\(\int x \cos ^3 x d x\)
Solution:

Question 27.
\(\int x \tan ^2 x d x\)
Solution:

Question 28.
\(\int x\left(\frac{\sec 2 x-1}{\sec 2 x+1}\right) d x\)
Solution:

Question 29.
\(\int \tan ^{-1}\left(\frac{2 x}{1-x^2}\right) d x\)
Solution:

Question 30.
\(\int \cos ^{-1} \frac{1-x^2}{1+x^2} d x\)
Solution:

Question 31.
\(\int\left(\tan ^{-1} x^2\right) x d x\)
Solution:

Question 32.
\(\int \sec ^{-1} \sqrt{x} d x\)
Solution:

Question 33.
\(\int \frac{\log \left(\sec ^{-1} x\right)}{x \sqrt{\left(x^2-1\right)}} d x\)
Solution:

Question 34.
\(\int e^x(1+x) \log \left(x e^x\right) d x\)
Solution:

Question 35.
\(\int \sin ^{-1}\left(3 x-4 x^3\right) d x\)
Solution:

Question 36.
\(\int \frac{x^2 \tan ^{-1} x}{1+x^2} d x\)
Solution: