What is the integral of 1/(\sqrt[3]{5^x)} ?

The integral of 1/(\sqrt[3]{5^x)} is -3/(ln(5)*5^{x/3)}+C

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integral of 1/(\sqrt[3]{5^x)}

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

Solution steps

Apply u-substitution

Take the constant out:

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

Simplify

= \frac{1}{ln ( 5 )} \cdot \int \frac{1}{u ^{\frac{4}{3}}} d u

Apply the Power Rule

Substitute back

u = 5^{x}

Simplify

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

Add a constant to the solution

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

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What is the integral of 1/(\sqrt[3]{5^x)} ?
The integral of 1/(\sqrt[3]{5^x)} is -3/(ln(5)*5^{x/3)}+C