What is the integral of \sqrt[3]{7^{5x}} ?

The integral of \sqrt[3]{7^{5x}} is 3/5*(7^{(5x)/3})/(ln(7))+C

Popular >

integral of \sqrt[3]{7^{5x}}

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

Solution steps

Apply radical rule:

assuming

a \geq 0

= \int 7^{\frac{5 x}{3}} d x

Apply u-substitution

: \int 7^{u} \cdot \frac{3}{5} d u

= \int 7^{u} \cdot \frac{3}{5} d u

Take the constant out:

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

= \frac{3}{5} \cdot \int 7^{u} d u

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

= \frac{3}{5} \cdot \frac{7 ^{u}}{ln ( 7 )}

Substitute back

u = \frac{5 x}{3}

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

Add a constant to the solution

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

\int π (\frac{1}{x})^{2} d x

\int y e^{y} - e^{y} d y

\int \frac{2 - e ^{x}}{6 e ^{4 x}} d x

\int 1 + (\frac{2}{3} x^{- \frac{1}{3}})^{2} d x

\int \frac{5}{8 y - 7} d y

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