What is the integral of xe^{x^2+2} ?

The integral of xe^{x^2+2} is 1/2 e^{x^2+2}+C

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integral of xe^{x^2+2}

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

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

Solution steps

\int x e^{x^{2} + 2} 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} + 2

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

Add a constant to the solution

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

x \to 4 - lim (ln (x - 4))

\int - e^{- 4 x} d x

\frac{d}{d x} ((3 x + 4)^{2})

x \to - 2 lim (1 - 3 x)

arctan (x)

What is the integral of xe^{x^2+2} ?
The integral of xe^{x^2+2} is 1/2 e^{x^2+2}+C