First slide

Methods of integration

Question

$\int \frac{\cos e c^{2} (e^{\sqrt{x}}) e^{\sqrt{x}} d x}{\sqrt{x}} is equal to$

Moderate

A

$- 2 \cot e^{\sqrt{x}} + C$
B

$2 \cot e^{\sqrt{x}} + C$
C

$- 2 \cot \sqrt{e^{x}} + C$
D

$2 \cot \sqrt{e^{x}} + C$

Solution

$Let I = \int \frac{\cos e c^{2} (e^{\sqrt{x}}) e^{\sqrt{x}}}{\sqrt{x}} d x$
$Put e^{\sqrt{x}} = y$
$\begin{array}{l} 2 \frac{e^{\sqrt{x}}}{\sqrt{x}} d x = d y \\ I = 2 \int \cos e c^{2} y d y \\ = 2 (- \cot y) + C \\ I = - 2 \cot e^{\sqrt{x}} + C \end{array}$

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