What is the integral of x^{10}e^{x^{11}} ?

The integral of x^{10}e^{x^{11}} is 1/11 e^{x^{11}}+C

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integral of x^{10}e^{x^{11}}

\int x^{10} e^{x^{11}} d x

\frac{1}{11} e^{x^{11}} + C

Solution steps

\int x^{10} e^{x^{11}} d x

Apply u-substitution

: \int \frac{e ^{u^{\frac{11}{10}}} u ^{\frac{1}{10}}}{10} d u

= \int \frac{e ^{u^{\frac{11}{10}}} u ^{\frac{1}{10}}}{10} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int e^{u^{\frac{11}{10}}} u^{\frac{1}{10}} d u

Apply u-substitution

: \int \frac{10 e ^{v}}{11} d v

= \frac{1}{10} \cdot \int \frac{10 e ^{v}}{11} d v

Take the constant out:

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

= \frac{1}{10} \cdot \frac{10}{11} \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{10} \cdot \frac{10}{11} e^{v}

Substitute back

= \frac{1}{10} \cdot \frac{10}{11} e^{(x^{10})^{\frac{11}{10}}}

Simplify

\frac{1}{10} \cdot \frac{10}{11} e^{(x^{10})^{\frac{11}{10}}} : \frac{1}{11} e^{x^{11}}

= \frac{1}{11} e^{x^{11}}

Add a constant to the solution

= \frac{1}{11} e^{x^{11}} + C

\frac{d}{d x} (7 sin^{2} (x))

f (x) = 1 - 3 x, at x = - 1

\frac{d}{d x} (\frac{3 x ^{2} - 1}{x - 2})

f (x) = sec (x), at x = (\frac{π}{3})

x \to - 1 lim (a r cos (x))

What is the integral of x^{10}e^{x^{11}} ?
The integral of x^{10}e^{x^{11}} is 1/11 e^{x^{11}}+C