What is the integral of (x^{11}e^{x^{12}}) ?

The integral of (x^{11}e^{x^{12}}) is 1/12 e^{x^{12}}+C

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integral of (x^{11}e^{x^{12}})

\int (x^{11} e^{x^{12}}) d x

\frac{1}{12} e^{x^{12}} + C

Solution steps

\int x^{11} e^{x^{12}} d x

Apply u-substitution

: \int \frac{e ^{u^{\frac{12}{11}}} u ^{\frac{1}{11}}}{11} d u

= \int \frac{e ^{u^{\frac{12}{11}}} u ^{\frac{1}{11}}}{11} d u

Take the constant out:

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

= \frac{1}{11} \cdot \int e^{u^{\frac{12}{11}}} u^{\frac{1}{11}} d u

Apply u-substitution

: \int \frac{11 e ^{v}}{12} d v

= \frac{1}{11} \cdot \int \frac{11 e ^{v}}{12} d v

Take the constant out:

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

= \frac{1}{11} \cdot \frac{11}{12} \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{11} \cdot \frac{11}{12} e^{v}

Substitute back

= \frac{1}{11} \cdot \frac{11}{12} e^{(x^{11})^{\frac{12}{11}}}

Simplify

\frac{1}{11} \cdot \frac{11}{12} e^{(x^{11})^{\frac{12}{11}}} : \frac{1}{12} e^{x^{12}}

= \frac{1}{12} e^{x^{12}}

Add a constant to the solution

= \frac{1}{12} e^{x^{12}} + C

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

2 x + y^{2} = 8, x

\frac{\partial}{\partial y} (sin (y))

\frac{d}{d x} (ln (x + sin (x) + 1))

y = \frac{( x ^{2} + 1 ) ^{5}}{( 1 - x ^{2} ) ^{5}}

What is the integral of (x^{11}e^{x^{12}}) ?
The integral of (x^{11}e^{x^{12}}) is 1/12 e^{x^{12}}+C