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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int \frac{e ^{u^{\frac{4}{3}}} u ^{\frac{1}{3}}}{3} d u

= \int \frac{e ^{u^{\frac{4}{3}}} u ^{\frac{1}{3}}}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int e^{u^{\frac{4}{3}}} u^{\frac{1}{3}} d u

Apply u-substitution

: \int \frac{3 e ^{v}}{4} d v

= \frac{1}{3} \cdot \int \frac{3 e ^{v}}{4} d v

Take the constant out:

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

= \frac{1}{3} \cdot \frac{3}{4} \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{3} \cdot \frac{3}{4} e^{v}

Substitute back

= \frac{1}{3} \cdot \frac{3}{4} e^{(y^{3})^{\frac{4}{3}}}

Simplify

\frac{1}{3} \cdot \frac{3}{4} e^{(y^{3})^{\frac{4}{3}}} : \frac{1}{4} e^{y^{4}}

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

Add a constant to the solution

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

\frac{d}{d x} (cos ((π x)^{9}))

\frac{\partial}{\partial x} (x^{0.1})

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

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 7, y^{^{'}} (0) = 0

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