What is the integral of (2x+1)sin(x^2+x) ?

The integral of (2x+1)sin(x^2+x) is -cos(x^2+x)+C

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integral of (2x+1)sin(x^2+x)

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

- cos (x^{2} + x) + C

Solution steps

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

Apply u-substitution

= \int sin (u) d u

Use the common integral:

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

= - cos (u)

Substitute back

u = x^{2} + x

= - cos (x^{2} + x)

Add a constant to the solution

= - cos (x^{2} + x) + C

What is the integral of (2x+1)sin(x^2+x) ?
The integral of (2x+1)sin(x^2+x) is -cos(x^2+x)+C