What is the integral of f(x)=x^3e^{x^{4+2}} ?

The integral of f(x)=x^3e^{x^{4+2}} is

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integral of f(x)=x^3e^{x^{4+2}}

integral

f (x) = x^{3} e^{x^{4 + 2}}

Solution steps

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

Apply u-substitution

: \int \frac{e ^{u^{3}} u}{2} d u

= \int \frac{e ^{u^{3}} 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^{3}} u d u

Apply u-substitution

: \int \frac{e ^{v^{\frac{3}{2}}}}{2} d v

= \frac{1}{2} \cdot \int \frac{e ^{v^{\frac{3}{2}}}}{2} d v

Take the constant out:

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

= \frac{1}{2} \cdot \frac{1}{2} \cdot \int e^{v^{\frac{3}{2}}} d v

Use the nonelementary integral:

Substitute back

Add a constant to the solution

\int \frac{2 x - 3}{x ^{2} + 2 x + 5} d x

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\int \frac{24 x}{4 x ^{2} + 1} d x

\int \frac{- 1}{4 x} d x

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

What is the integral of f(x)=x^3e^{x^{4+2}} ?
The integral of f(x)=x^3e^{x^{4+2}} is