What is the integral of 17ln(\sqrt[3]{x}) ?

The integral of 17ln(\sqrt[3]{x}) is 17(1/3 xln(x)-1/3 x)+C

Popular >

integral of 17ln(\sqrt[3]{x})

\int 17 ln (3 x) d x

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

Solution steps

\int 17 ln (3 x) d x

Take the constant out:

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

= 17 \cdot \int ln (3 x) d x

Apply Integration By Parts

= 17 (x ln (3 x) - \int \frac{1}{3} d x)

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

= 17 (x ln (3 x) - \frac{1}{3} x)

Simplify

ln (3 x) : \frac{1}{3} ln (x)

= 17 (\frac{1}{3} x ln (x) - \frac{1}{3} x)

Add a constant to the solution

= 17 (\frac{1}{3} x ln (x) - \frac{1}{3} x) + C

\int \frac{x ^{3} - 5 x ^{2} - 2}{x ^{3}} d x

\frac{9 - x ^{2}}{8 x}

\frac{d ^{4}}{d x ^{4}} (\frac{10 x}{1 - x})

f (x) = e^{5 x^{2}}

y = sin (2 x), at x = \frac{π}{2}

What is the integral of 17ln(\sqrt[3]{x}) ?
The integral of 17ln(\sqrt[3]{x}) is 17(1/3 xln(x)-1/3 x)+C