What is the integral of 14ln(\sqrt[3]{x}) ?

The integral of 14ln(\sqrt[3]{x}) is 14(1/3 xln(x)-1/3 x)+C

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integral of 14ln(\sqrt[3]{x})

\int 14 ln (3 x) d x

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

Solution steps

\int 14 ln (3 x) d x

Take the constant out:

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

= 14 \cdot \int ln (3 x) d x

Apply Integration By Parts

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

= 14 (x ln (3 x) - \int \frac{1}{3} d x)

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

= 14 (x ln (3 x) - \frac{1}{3} x)

Simplify

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

= 14 (\frac{1}{3} x ln (x) - \frac{1}{3} x)

Add a constant to the solution

= 14 (\frac{1}{3} x ln (x) - \frac{1}{3} x) + C

y = \frac{7}{x} + 6 sec (x)

\frac{\partial}{\partial y} (\frac{3 x}{( x + y ) ^{4}})

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

f^{^{'}} (x) = 3 e^{x} + 7 sec^{2} (x)

2 y^{^{''}} + y^{^{'}} - y = x + 5

What is the integral of 14ln(\sqrt[3]{x}) ?
The integral of 14ln(\sqrt[3]{x}) is 14(1/3 xln(x)-1/3 x)+C