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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int u cos (u^{2}) d u

= \int u cos (u^{2}) d u

Apply u-substitution

: \int \frac{cos ( v )}{2} d v

= \int \frac{cos ( v )}{2} d v

Take the constant out:

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

= \frac{1}{2} \cdot \int cos (v) d v

Use the common integral:

\int cos (v) d v = sin (v)

= \frac{1}{2} sin (v)

Substitute back

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

Add a constant to the solution

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

\frac{d}{d x} (6 x^{2} - 18 x + 12)

x^{2}, - 4, 0

\int x^{5} x^{3} + 4 d x

\int_{0}^{\frac{π}{21}} tan (7 x) d x

y^{^{'}} + 2 y = 1

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