Question

Integrate the function : x sin x

Answer 1

Answer:

$\bf\int{x\:sinx}\:dx=-x\:cosx+sinx+C$

Step-by-step explanation:

Integrate the function : x sin x

I have applied integration by parts method to solve this integral

$\int{x\:sinx}\:dx$

Take

$u=x$

$\frac{du}{dx}=1$

$\implies\:du=dx$

and

$dv=sinx\:dx$

$\int{dv}=\int{sinx}\:dx$

$\implies\:v=-cosx$

Using

$\boxed{\int{u}\:dv=uv-\int{v}\:du}$

$\int{x\:sinx}\:dx=x(-cosx)-\int{(-cosx)\:dx}$

$\int{x\:sinx}\:dx=-x\:cosx+\int{cosx}\:dx$

$\implies\:\boxed{\int{x\:sinx}\:dx=-x\:cosx+sinx+C}$