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 \cdot 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 8 - 4 x^{2} d x

\int (x^{2} + x)^{8} (2 x + 1) d x

\int x x^{2} + 1 d x

\int \frac{1}{( x + 2 ) ( x ^{2} + 2 x + 4 ) ^{2}} d x

\int 4 y d y

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