What is the integral of (2x+2)e^{x^2+2x} ?

The integral of (2x+2)e^{x^2+2x} is e^{x^2+2x}+C

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integral of (2x+2)e^{x^2+2x}

\int (2 x + 2) e^{x^{2} + 2 x} d x

e^{x^{2} + 2 x} + C

Solution steps

\int (2 x + 2) e^{x^{2} + 2 x} d x

Apply u-substitution

: \int e^{u} d u

= \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= e^{u}

Substitute back

u = x^{2} + 2 x

= e^{x^{2} + 2 x}

Add a constant to the solution

= e^{x^{2} + 2 x} + C

\int y^{3} d y

\int_{0}^{1} \frac{3 x ^{3}}{4 x ^{4} + 9} d x

\frac{d}{d x} (\frac{2}{( 2 - x ^{8} ) ^{\frac{3}{2}}})

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

\frac{1}{4 x}

What is the integral of (2x+2)e^{x^2+2x} ?
The integral of (2x+2)e^{x^2+2x} is e^{x^2+2x}+C