What is the integral of (x^6e^{x^7}) ?

The integral of (x^6e^{x^7}) is 1/7 e^{x^7}+C

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integral of (x^6e^{x^7})

\int (x^{6} e^{x^{7}}) d x

\frac{1}{7} e^{x^{7}} + C

Solution steps

\int x^{6} e^{x^{7}} d x

Apply u-substitution

: \int \frac{e ^{u^{\frac{7}{6}}} u ^{\frac{1}{6}}}{6} d u

= \int \frac{e ^{u^{\frac{7}{6}}} u ^{\frac{1}{6}}}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int e^{u^{\frac{7}{6}}} u^{\frac{1}{6}} d u

Apply u-substitution

: \int \frac{6 e ^{v}}{7} d v

= \frac{1}{6} \cdot \int \frac{6 e ^{v}}{7} d v

Take the constant out:

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

= \frac{1}{6} \cdot \frac{6}{7} \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{6} \cdot \frac{6}{7} e^{v}

Substitute back

= \frac{1}{6} \cdot \frac{6}{7} e^{(x^{6})^{\frac{7}{6}}}

Simplify

\frac{1}{6} \cdot \frac{6}{7} e^{(x^{6})^{\frac{7}{6}}} : \frac{1}{7} e^{x^{7}}

= \frac{1}{7} e^{x^{7}}

Add a constant to the solution

= \frac{1}{7} e^{x^{7}} + C

\int \frac{8 x + 12}{x \cdot ( x ^{2} + 4 )} d x

\frac{\partial}{\partial x} (x 1 + y^{3})

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

3 x^{2} - 1, at x = - 2

y = \frac{x ^{2} + 2}{x + 8}, (3, 1)

What is the integral of (x^6e^{x^7}) ?
The integral of (x^6e^{x^7}) is 1/7 e^{x^7}+C