What is the integral of x^37^{x^4} ?

The integral of x^37^{x^4} is 1/(4ln(7))*7^{x^4}+C

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integral of x^37^{x^4}

\int x^{3} 7^{x^{4}} d x

\frac{1}{4 ln ( 7 )} \cdot 7^{x^{4}} + C

Solution steps

\int x^{3} \cdot 7^{x^{4}} d x

Apply u-substitution

: \int \frac{1}{4 ln ( 7 )} d u

= \int \frac{1}{4 ln ( 7 )} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{4 ln ( 7 )} u

Substitute back

u = 7^{x^{4}}

= \frac{1}{4 ln ( 7 )} \cdot 7^{x^{4}}

Add a constant to the solution

= \frac{1}{4 ln ( 7 )} \cdot 7^{x^{4}} + C

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What is the integral of x^37^{x^4} ?
The integral of x^37^{x^4} is 1/(4ln(7))*7^{x^4}+C