What is the integral of xe^{4x^2+3} ?

The integral of xe^{4x^2+3} is 1/8 e^{4x^2+3}+C

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integral of xe^{4x^2+3}

\int x e^{4 x^{2} + 3} d x

\frac{1}{8} e^{4 x^{2} + 3} + C

Solution steps

\int x e^{4 x^{2} + 3} d x

Apply u-substitution

: \int \frac{e ^{u}}{8} d u

= \int \frac{e ^{u}}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{8} e^{u}

Substitute back

u = 4 x^{2} + 3

= \frac{1}{8} e^{4 x^{2} + 3}

Add a constant to the solution

= \frac{1}{8} e^{4 x^{2} + 3} + C

\int e^{a x} sin (2 x) d x

\int (2 x - 1) d x

\int cos (x) 3 d x

\int (\frac{1}{x - 3}) d x

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What is the integral of xe^{4x^2+3} ?
The integral of xe^{4x^2+3} is 1/8 e^{4x^2+3}+C