Continuous practice using ISC Class 12 Maths Solutions OP Malhotra Chapter 14 Indefinite Integral-2 Ex 14(e) can lead to a stronger grasp of mathematical concepts.
S Chand Class 12 ICSE Maths Solutions Chapter 14 Indefinite Integral-2 Ex 14(e)
Question 1.
Evaluate:
\(\int e^x(\cot x+\log \sin x) d x\)
Solution:
Question 2.
\(\int e^{2 x}(-\sin x+2 \cos x) d x\)
Solution:
Question 3.
\(\int e^x(\tan x+\log \sec x) d x \text { or } \int e^x(\tan x-\log \cos x) d x\)
Solution:
Question 4.
\(\int\{\sin (\log x)+\cos (\log x)\} d x\)
Solution:
Question 5.
\(\int\left\{\tan (\log x)+\sec ^2(\log x)\right\} d x\)
Solution:
Question 6.
\(\int e^x\left(\sin ^{-1} x+\frac{1}{\sqrt{1-x^2}}\right) d x\)
Solution:
Question 7.
\(\int e^x[\sec x+\log (\sec x+\tan x)] d x\)
Solution:
Question 8.
\(\int e^x \frac{1-\sin x}{1-\cos x} d x\)
Solution:
Question 9.
\(\int e^x \frac{2-\sin 2 x}{1-\cos 2 x} d x\)
Solution:
Question 10.
\(\int\left(\log (\log x)+\frac{1}{\log x}\right) d x\)
Solution:
Question 11.
\(\int \frac{\log x}{(1+\log x)^2} d x\)
Solution:
Question 12.
\(\int \frac{1-x}{x^2} e^x d x\)
Solution:
Question 13.
\(\int e^{2 x}\left(\frac{2 x-1}{4 x^2}\right) d x\)
Solution:
Question 14.
\(\int e^x\left(\frac{1}{x^2}-\frac{2}{x^3}\right) d x\)
Solution:
Question 15.
\(\int \frac{x+\sin x}{1+\cos x} d x\)
Solution:
Question 16.
\(\int e^x\left(\frac{1-x}{1+x^2}\right)^2 d x\)
Solution:
