What is the integral of (x+4)e^{x^2+8x} ?

The integral of (x+4)e^{x^2+8x} is 1/2 e^{x^2+8x}+C

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integral of (x+4)e^{x^2+8x}

\int (x + 4) e^{x^{2} + 8 x} d x

\frac{1}{2} e^{x^{2} + 8 x} + C

Solution steps

\int (x + 4) e^{x^{2} + 8 x} d x

Apply u-substitution

: \int \frac{e ^{u}}{2} d u

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

Use the common integral:

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

= \frac{1}{2} e^{u}

Substitute back

u = x^{2} + 8 x

= \frac{1}{2} e^{x^{2} + 8 x}

Add a constant to the solution

= \frac{1}{2} e^{x^{2} + 8 x} + C

(6 x + 1) y^{2} (\frac{d y}{d x}) + 3 x^{2} + 2 y^{3} = 0

y = x^{2} cos (x)

\frac{d y}{d x} = 4 x 4 - y^{2}

\int x sin (ln (x)) d x

\int_{4}^{\infty} e^{- \frac{x}{2}} d x

What is the integral of (x+4)e^{x^2+8x} ?
The integral of (x+4)e^{x^2+8x} is 1/2 e^{x^2+8x}+C