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

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

= \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

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