What is the integral of 2\sqrt[5]{x^3}-3sqrt(x) ?

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

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integral of 2\sqrt[5]{x^3}-3sqrt(x)

\frac{5}{4} x^{\frac{8}{5}} - 2 x^{\frac{3}{2}} + C

Solution steps

assuming

x \geq 0

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

\int 2 x^{\frac{3}{5}} d x = \frac{5}{4} x^{\frac{8}{5}}

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

= \frac{5}{4} x^{\frac{8}{5}} - 2 x^{\frac{3}{2}}

Add a constant to the solution

= \frac{5}{4} x^{\frac{8}{5}} - 2 x^{\frac{3}{2}} + C

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

\frac{d y}{d x} = \frac{x ( e ^{x^{2}} + 2 )}{6 y ^{2}}

y = (6 x - 2) (5 x + 7)

\int_{0}^{4 π} t^{2} sin (2 t) d t

\int 2^{4 x} d x

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