What is the integral of (x)(sin(x)) ?

The integral of (x)(sin(x)) is -xcos(x)+sin(x)+C

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integral of (x)(sin(x))

\int (x) (sin (x)) d x

- x cos (x) + sin (x) + C

Solution steps

\int x sin (x) d x

Apply Integration By Parts

: - x cos (x) - \int - cos (x) d x

= - x cos (x) - \int - cos (x) d x

\int - cos (x) d x = - sin (x)

= - x cos (x) - (- sin (x))

Simplify

= - x cos (x) + sin (x)

Add a constant to the solution

= - x cos (x) + sin (x) + C

\int - x^{2} + 4 x d x

\int e^{- 2 θ} sin (3 θ) d θ

\int 6 x - \frac{3}{x} d x

cos (6 x)

\int \frac{x - 4}{x ^{3}} d x

What is the integral of (x)(sin(x)) ?
The integral of (x)(sin(x)) is -xcos(x)+sin(x)+C