What is the integral of 10x^5e^{x^6} ?

The integral of 10x^5e^{x^6} is 5/3 e^{x^6}+C

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integral of 10x^5e^{x^6}

\int 10 x^{5} e^{x^{6}} d x

\frac{5}{3} e^{x^{6}} + C

Solution steps

\int 10 x^{5} e^{x^{6}} d x

Take the constant out:

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

= 10 \cdot \int x^{5} e^{x^{6}} d x

Apply u-substitution

: \int \frac{e ^{u^{\frac{6}{5}}} u ^{\frac{1}{5}}}{5} d u

= 10 \cdot \int \frac{e ^{u^{\frac{6}{5}}} u ^{\frac{1}{5}}}{5} d u

Take the constant out:

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

= 10 \cdot \frac{1}{5} \cdot \int e^{u^{\frac{6}{5}}} u^{\frac{1}{5}} d u

Apply u-substitution

: \int \frac{5 e ^{v}}{6} d v

= 10 \cdot \frac{1}{5} \cdot \int \frac{5 e ^{v}}{6} d v

Take the constant out:

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

= 10 \cdot \frac{1}{5} \cdot \frac{5}{6} \cdot \int e^{v} d v

Use the common integral:

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

= 10 \cdot \frac{1}{5} \cdot \frac{5}{6} e^{v}

Substitute back

= 10 \cdot \frac{1}{5} \cdot \frac{5}{6} e^{(x^{5})^{\frac{6}{5}}}

Simplify

10 \cdot \frac{1}{5} \cdot \frac{5}{6} e^{(x^{5})^{\frac{6}{5}}} : \frac{5}{3} e^{x^{6}}

= \frac{5}{3} e^{x^{6}}

Add a constant to the solution

= \frac{5}{3} e^{x^{6}} + C

\frac{\partial}{\partial x} (ln (e^{x} + e^{- x}))

\frac{\partial}{\partial x} (\frac{1}{a} e^{- (\frac{x}{a})^{2}})

f (x) = 8 x^{2} + 3 x, at x = - 45

\frac{d y}{d x} = 2 sec^{2} (x) e^{2 y}, y (0) = 0

x \to 3 lim (\frac{x - 2 - 1}{x - 3})

What is the integral of 10x^5e^{x^6} ?
The integral of 10x^5e^{x^6} is 5/3 e^{x^6}+C