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

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

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integral of x^3e^{2x^4}

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

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

Solution steps

\int x^{3} e^{2 x^{4}} 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 = 2 x^{4}

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

Add a constant to the solution

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

y = e^{x} (x^{2} - 3)

\int sin (8 π t) d t

\frac{d}{d x} (x ln (2 x + 3))

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

(1 + x)^{2}

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