Question

What is $\int (x\cos x+\sin x)dx$ equal to?

Where $c$ is an arbitrary constant

• A. $x\sin x+c$
• B. $x\cos x+c$
• C. $-x\sin x+c$
• D. $-x\cos x+c$
  

Answer 1

The correct option is A $x\sin x+c$

$\int (x.\cos x+\sin x)dx$

$=\int x.\cos x.dx+\int \sin x.dx$

By u\sin g uv rule for integration in the first integral taking x as first function and \cos x as second we have,

$=x.\sin x-\int \sin x.dx+\int \sin x.dx+c$

$=x.\sin x+c$

Hence, A is correct.