What is the integral of 28x^6e^{x^7} ?

The integral of 28x^6e^{x^7} is 4e^{x^7}+C

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integral of 28x^6e^{x^7}

\int 28 x^{6} e^{x^{7}} d x

4 e^{x^{7}} + C

Solution steps

\int 28 x^{6} e^{x^{7}} d x

Take the constant out:

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

= 28 \cdot \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

= 28 \cdot \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

= 28 \cdot \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

= 28 \cdot \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

= 28 \cdot \frac{1}{6} \cdot \frac{6}{7} \cdot \int e^{v} d v

Use the common integral:

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

= 28 \cdot \frac{1}{6} \cdot \frac{6}{7} e^{v}

Substitute back

= 28 \cdot \frac{1}{6} \cdot \frac{6}{7} e^{(x^{6})^{\frac{7}{6}}}

Simplify

28 \cdot \frac{1}{6} \cdot \frac{6}{7} e^{(x^{6})^{\frac{7}{6}}} : 4 e^{x^{7}}

= 4 e^{x^{7}}

Add a constant to the solution

= 4 e^{x^{7}} + C

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What is the integral of 28x^6e^{x^7} ?
The integral of 28x^6e^{x^7} is 4e^{x^7}+C