First slide

Methods of integration

Question

$\int \frac{\cos e c \log \sqrt{x}}{x} d x is equal to$

Moderate

A

$- 2 \log |\cos e c \log \sqrt{x} + cotlog \sqrt{x}| + C$
B

$2 \log |\cos e c \log \sqrt{x} + cotlog \sqrt{x}| + C$
C

$2 \log |\cos e c \log \sqrt{x} - cotlog \sqrt{x}| + C$
D

$- 2 \log |\cos e c \log - cotlog \sqrt{x}| + C$

Solution

$Let I = \int \frac{\cos e c \log \sqrt{x}}{x} d x$
$Put \log \sqrt{x} = y$
$\begin{array}{l} \frac{1 d x}{\sqrt{x} 2 \sqrt{x}} = d y \\ \frac{d x}{x} = 2 d y \\ I = 2 \int \cos e c y d y \\ = 2 \log | cosecy - \cot y | + C \\ I = 2 \log | cosec \log \sqrt{x} - \cot \log \sqrt{x} | + C \end{array}$

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