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

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

Popular >

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

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

- \frac{1}{2} cos (x^{2} + 2 x) + C

Solution steps

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

Apply u-substitution

: \int \frac{sin ( u )}{2} d u

= \int \frac{sin ( u )}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{2} (- cos (u))

Substitute back

u = x^{2} + 2 x

= \frac{1}{2} (- cos (x^{2} + 2 x))

Simplify

= - \frac{1}{2} cos (x^{2} + 2 x)

Add a constant to the solution

= - \frac{1}{2} cos (x^{2} + 2 x) + C

x \to 1 lim (sin (5 π x))

\int (3 t + 2)^{2.4} d t

\frac{\partial}{\partial x} (cos (x) cosh (y))

x^{4} e^{x} - 5

\int 3 x^{2} \times 4 x^{4} d x

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