What is the integral of (x+1)sin(x) ?

The integral of (x+1)sin(x) is -cos(x)(x+1)+sin(x)+C

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integral of (x+1)sin(x)

\int (x + 1) sin (x) d x

- cos (x) (x + 1) + sin (x) + C

Solution steps

\int (x + 1) sin (x) d x

Apply Integration By Parts

= - cos (x) (x + 1) - \int - cos (x) d x

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

= - cos (x) (x + 1) - (- sin (x))

Simplify

= - cos (x) (x + 1) + sin (x)

Add a constant to the solution

= - cos (x) (x + 1) + sin (x) + C

\int \frac{sin ( x )}{1 + sin ( x ) + cos ( x )} d x

\int \frac{5}{x ( ln ( x ) ) ^{4}} d x

\int \frac{1}{x ( x ^{7} + 1 )} d x

\int \frac{125}{( 5 x - 300 ) ^{2}} d x

\int \frac{3}{1 + 9 x ^{2}} d x

What is the integral of (x+1)sin(x) ?
The integral of (x+1)sin(x) is -cos(x)(x+1)+sin(x)+C