What is the integral of 8^{3x^3}5x^2 ?

The integral of 8^{3x^3}5x^2 is (5*512^{x^3})/(27ln(2))+C

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integral of 8^{3x^3}5x^2

\int 8^{3 x^{3}} 5 x^{2} d x

\frac{5 \cdot 51 2 ^{x^{3}}}{27 ln ( 2 )} + C

Solution steps

\int 8^{3 x^{3}} \cdot 5 x^{2} d x

Take the constant out:

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

= 5 \cdot \int 8^{3 x^{3}} x^{2} d x

Apply u-substitution

: \int \frac{51 2 ^{u}}{3} d u

= 5 \cdot \int \frac{51 2 ^{u}}{3} d u

Take the constant out:

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

= 5 \cdot \frac{1}{3} \cdot \int 51 2^{u} d u

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

= 5 \cdot \frac{1}{3} \cdot \frac{51 2 ^{u}}{ln ( 512 )}

Substitute back

u = x^{3}

= 5 \cdot \frac{1}{3} \cdot \frac{51 2 ^{x^{3}}}{ln ( 512 )}

Simplify

5 \cdot \frac{1}{3} \cdot \frac{51 2 ^{x^{3}}}{ln ( 512 )} : \frac{5 \cdot 51 2 ^{x^{3}}}{27 ln ( 2 )}

= \frac{5 \cdot 51 2 ^{x^{3}}}{27 ln ( 2 )}

Add a constant to the solution

= \frac{5 \cdot 51 2 ^{x^{3}}}{27 ln ( 2 )} + C

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What is the integral of 8^{3x^3}5x^2 ?
The integral of 8^{3x^3}5x^2 is (5*512^{x^3})/(27ln(2))+C