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

The integral of (6sqrt(x^3)+7\sqrt[3]{x^2}) is 12/5 x^{5/2}+21/5 x^{5/3}+C

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

\int (6 x^{3} + 7 3 x^{2}) d x

\frac{12}{5} x^{\frac{5}{2}} + \frac{21}{5} x^{\frac{5}{3}} + C

Solution steps

\int 6 x^{3} + 7 3 x^{2} d x

Apply the Sum Rule:

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

= \int 6 x^{3} d x + \int 7 3 x^{2} d x

\int 6 x^{3} d x = \frac{12}{5} x^{\frac{5}{2}}

\int 7 3 x^{2} d x = \frac{21}{5} x^{\frac{5}{3}}

= \frac{12}{5} x^{\frac{5}{2}} + \frac{21}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{12}{5} x^{\frac{5}{2}} + \frac{21}{5} x^{\frac{5}{3}} + C

y = sec^{2} (x), y = sin (x), [0, \frac{π}{4}]

\int \frac{10 sin ( t )}{- 3 + 6 cos ( t )} d t

x \to 0 lim (e^{\frac{x}{x ^{2} - 4}})

x \to 7 - lim (\frac{( 2 x + 1 )}{x - 7})

\frac{\partial}{\partial x} (\frac{7 y - 4 x}{y ^{2} + 2 x ^{2}})

What is the integral of (6sqrt(x^3)+7\sqrt[3]{x^2}) ?
The integral of (6sqrt(x^3)+7\sqrt[3]{x^2}) is 12/5 x^{5/2}+21/5 x^{5/3}+C