What is the integral of 40x^{3/2}-60x^2 ?

The integral of 40x^{3/2}-60x^2 is 16x^{5/2}-20x^3+C

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integral of 40x^{3/2}-60x^2

\int 40 x^{\frac{3}{2}} - 60 x^{2} d x

16 x^{\frac{5}{2}} - 20 x^{3} + C

Solution steps

\int 40 x^{\frac{3}{2}} - 60 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 40 x^{\frac{3}{2}} d x - \int 60 x^{2} d x

\int 40 x^{\frac{3}{2}} d x = 16 x^{\frac{5}{2}}

\int 60 x^{2} d x = 20 x^{3}

= 16 x^{\frac{5}{2}} - 20 x^{3}

Add a constant to the solution

= 16 x^{\frac{5}{2}} - 20 x^{3} + C

\frac{4}{t ^{2}}

\frac{s}{s ^{2} + s + 3}

\frac{d}{d x} (\frac{4}{3} π r (x) (x)^{3})

\frac{d}{d x} (\frac{- x ^{2} - 8}{( x ^{2} - 8 ) ^{2}})

\frac{d x}{d t} = - \frac{6 x}{20 + 2 t}

What is the integral of 40x^{3/2}-60x^2 ?
The integral of 40x^{3/2}-60x^2 is 16x^{5/2}-20x^3+C