Deepak Scored 45->99%ile with Bounce Back Crack Course. You can do it too!

Evaluate the following integrals:

Question:

Evaluate the following integrals:

$\int \frac{e^{\sqrt{x}} \cos \left(e^{\sqrt{x}}\right)}{\sqrt{x}} d x$

Solution:

Assume $e^{\sqrt{x}}=t$

$d\left(e^{\sqrt{x}}\right)=d t$

$\Rightarrow \frac{e^{\sqrt{x}}}{2 \sqrt{x}} d x=d t$

$\Rightarrow \frac{e^{\sqrt{x}}}{\sqrt{x}} d x=2 d t$

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

$\Rightarrow 2 \int \cos t d t$

$=2 \sin t+c$

But $t=e^{\sqrt{x}}$

$\Rightarrow 2 \sin \left(e^{\sqrt{x}}\right)+c$

Leave a comment

None
Free Study Material