What is the integral of (5x+2)/(\sqrt[3]{6x+3)} ?

The integral of (5x+2)/(\sqrt[3]{6x+3)} is (3^{2/3})/8 (4x-3)(2x+1)^{2/3}+1/2 (6x+3)^{2/3}+C

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integral of (5x+2)/(\sqrt[3]{6x+3)}

\frac{3 ^{\frac{2}{3}}}{8} (4 x - 3) (2 x + 1)^{\frac{2}{3}} + \frac{1}{2} (6 x + 3)^{\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

= \frac{3 ^{\frac{2}{3}}}{8} (4 x - 3) (2 x + 1)^{\frac{2}{3}} + \frac{1}{2} (6 x + 3)^{\frac{2}{3}}

Add a constant to the solution

= \frac{3 ^{\frac{2}{3}}}{8} (4 x - 3) (2 x + 1)^{\frac{2}{3}} + \frac{1}{2} (6 x + 3)^{\frac{2}{3}} + C

\frac{6}{( s - 2 ) ^{6}}

f (x) = \frac{π}{x}

\int \frac{42 x ^{7} - 7 x}{7 x ^{5}} d x

\int \frac{1}{2 x ^{6}} d x

f (x) = - x^{2} - 3 x + 4, at x = - 3

What is the integral of (5x+2)/(\sqrt[3]{6x+3)} ?
The integral of (5x+2)/(\sqrt[3]{6x+3)} is (3^{2/3})/8 (4x-3)(2x+1)^{2/3}+1/2 (6x+3)^{2/3}+C