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Popular >

integral of (4x-1)/(\sqrt[3]{3x+1)}

Solution

Solution

4 (\frac{1}{2} x (3 x + 1)^{\frac{2}{3}} - \frac{1}{10} (3 x + 1)^{\frac{5}{3}}) - \frac{1}{2} (3 x + 1)^{\frac{2}{3}} + C

Solution steps

Expand

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 4 (\frac{1}{2} x (3 x + 1)^{\frac{2}{3}} - \frac{1}{10} (3 x + 1)^{\frac{5}{3}}) - \frac{1}{2} (3 x + 1)^{\frac{2}{3}}

Add a constant to the solution

= 4 (\frac{1}{2} x (3 x + 1)^{\frac{2}{3}} - \frac{1}{10} (3 x + 1)^{\frac{5}{3}}) - \frac{1}{2} (3 x + 1)^{\frac{2}{3}} + C

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Frequently Asked Questions (FAQ)

What is the integral of (4x-1)/(\sqrt[3]{3x+1)} ?
The integral of (4x-1)/(\sqrt[3]{3x+1)} is 4(1/2 x(3x+1)^{2/3}-1/10 (3x+1)^{5/3})-1/2 (3x+1)^{2/3}+C