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Home  >>  CBSE XII  >>  Math  >>  Integrals
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Evaluate the following $\large\int\frac{(1+\cos x)}{x+\sin x}dx$

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Toolbox:
  • If $f(x)$ is substituted by t, then $f'(x)dx=f'(t)dt.$ Hence $\int f(x)dx=\int t.dt$
  • $\large\int \frac{dx}{x}=log |x|+c$
Let $I=\large\int\frac{(1+\cos x)}{x+\sin x}dx$
Let $x+\sin x=t$ Differentiating on both sides.
$(1+\cos x)dx=dt$ on substituting,
I can be written as
$I=\large\int \frac{dt}{t}$
On integrating we get
$I=log\; t+c$
Substituting for t we get
$I=log|x+\sin x|+c$
answered Apr 11, 2013 by meena.p
 
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