What is the integral of x^2*7^{x^3+5} ?

The integral of x^2*7^{x^3+5} is (7^{x^3+5})/(3ln(7))+C

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integral of x^2*7^{x^3+5}

\int x^{2} \cdot 7^{x^{3} + 5} d x

\frac{7 ^{x^{3} + 5}}{3 ln ( 7 )} + C

Solution steps

\int x^{2} \cdot 7^{x^{3} + 5} d x

Apply u-substitution

: \int \frac{7 ^{u}}{3} d u

= \int \frac{7 ^{u}}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int 7^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{1}{3} \cdot \frac{7 ^{u}}{ln ( 7 )}

Substitute back

u = x^{3} + 5

= \frac{1}{3} \cdot \frac{7 ^{x^{3} + 5}}{ln ( 7 )}

Simplify

\frac{1}{3} \cdot \frac{7 ^{x^{3} + 5}}{ln ( 7 )} : \frac{7 ^{x^{3} + 5}}{3 ln ( 7 )}

= \frac{7 ^{x^{3} + 5}}{3 ln ( 7 )}

Add a constant to the solution

= \frac{7 ^{x^{3} + 5}}{3 ln ( 7 )} + C

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What is the integral of x^2*7^{x^3+5} ?
The integral of x^2*7^{x^3+5} is (7^{x^3+5})/(3ln(7))+C