If I=∫(\frac{x^2dx}{(x,sin,x+cos,x)^2})=f(x)+tan x+c, then f... | Mathematics | SolveeIt | Solveeit

Today, August 19

Question

If I=∫ $\frac{x^2dx}{(x\,sin\,x+cos\,x)^2}$ =f(x)+tan x+c, then f(x) is

A

$\frac{sin\,x}{xsin\,x+cos\,x}$

B

$\frac{1}{(xsin\,x+cos\,x)^2}$

C

$\frac{-x}{cos\,x(xsin\,x+cos\,x)}$

D

$\frac{1}{sin\,x(xcos\,x+sin\,x)}$

Answer

$\frac{-x}{cos\,x(xsin\,x+cos\,x)}$

Explanation

Solution

The correct answer is option (C): $\frac{-x}{cos\,x(xsin\,x+cos\,x)}$