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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int \frac{e ^{u}}{4} d u

= \int \frac{e ^{u}}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{4} e^{u}

Substitute back

u = x^{4}

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

Add a constant to the solution

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

\frac{d y}{d x} = x + 3

x \to 2 lim (4 x)

\int_{1}^{4} (\frac{1}{x})^{2} d x

y x + y^{2} = 2 x, (4, 2)

\frac{d}{d x} ((2 x^{2} - x - 1) x)

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