Question

$\int e^x(1-\cot x+{\cot }^{2}x)dx$ equals to

• A. $e^x\cot x+C$
• B. $e^x\cos ecx+C$
• C. $-e^x\cot x+C$
• D. $-e^x\cos ecx+C$

Answer 1

Answer: (C)

Let $x_1,x_2\in R$ such that $x_1<x_2$ . Then, $x_1<x_2$ $\Rightarrow$ $f(x_1)<f(x_2)$ ( $\because$ $f$ is an increasing function) $\Rightarrow$ $g\{f(x_1)\}<g\{f(x_2)\}$ ( $\because$ is an increasing function) $\Rightarrow$ $gof(x_1)<gof(x_2)$ Hence, $gof$ is an increasing function.