Evaluate the following integrals:

Question:

Evaluate the following integrals:

$\int \frac{e^{m \tan ^{-1} x}}{1+x^{2}} d x$

Solution:

Assume $\tan ^{-1} x=t$

$d\left(\tan ^{-1} x\right)=d t$

$\Rightarrow \frac{1}{x^{2}+1}=d t$

Substituting $\mathrm{t}$ and $\mathrm{dt}$

$\Rightarrow \int e^{m t} d t$

$\Rightarrow \frac{e^{m t}}{m}+c$

But $t=\tan ^{-1}_{x}$

$\Rightarrow \frac{\mathrm{e}^{\mathrm{mtan}^{-1} \mathrm{x}}}{\mathrm{m}}+\mathrm{c}$

Leave a comment

None
Free Study Material