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

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

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integral of 5ln(\sqrt[3]{x})

5 (\frac{1}{3} x ln (x) - \frac{1}{3} x) + C

Solution steps

Take the constant out:

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

Apply Integration By Parts

\int \frac{1}{3} d x = \frac{1}{3} x

Simplify

= 5 (\frac{1}{3} x ln (x) - \frac{1}{3} x)

Add a constant to the solution

= 5 (\frac{1}{3} x ln (x) - \frac{1}{3} x) + C

\int_{0}^{\frac{π}{2}} 42

y = x^{3} + 4 x - 3, (1, 2)

4 e^{a r c c o s (4 x)}

\int 3 x^{3} d x

f (x) = ln (x^{2} - 2 x + 1), at x = 2

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