What is the integral of 7sqrt(x^3)+6\sqrt[3]{x^2} ?

The integral of 7sqrt(x^3)+6\sqrt[3]{x^2} is 14/5 x^{5/2}+18/5 x^{5/3}+C

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integral of 7sqrt(x^3)+6\sqrt[3]{x^2}

\frac{14}{5} x^{\frac{5}{2}} + \frac{18}{5} x^{\frac{5}{3}} + C

Solution steps

Apply the Sum Rule:

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

\int 7 x^{3} d x = \frac{14}{5} x^{\frac{5}{2}}

= \frac{14}{5} x^{\frac{5}{2}} + \frac{18}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{14}{5} x^{\frac{5}{2}} + \frac{18}{5} x^{\frac{5}{3}} + C

\int \frac{x - 3}{3 x ^{2} + 6 x + 2} d x

\int (x^{2} + 2)^{3} x d x

\int \frac{5 x - 2}{( x + 2 ) ^{2}} d x

\int x^{2} e^{\frac{x}{3}} d x

\int \frac{( x ^{2} )}{x + 3} d x

What is the integral of 7sqrt(x^3)+6\sqrt[3]{x^2} ?
The integral of 7sqrt(x^3)+6\sqrt[3]{x^2} is 14/5 x^{5/2}+18/5 x^{5/3}+C