What is the integral of-4x^{3/2}+3x^{2/3}-4x^2 ?

The integral of-4x^{3/2}+3x^{2/3}-4x^2 is -8/5 x^{5/2}+9/5 x^{5/3}-(4x^3)/3+C

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integral of-4x^{3/2}+3x^{2/3}-4x^2

\int - 4 x^{\frac{3}{2}} + 3 x^{\frac{2}{3}} - 4 x^{2} d x

- \frac{8}{5} x^{\frac{5}{2}} + \frac{9}{5} x^{\frac{5}{3}} - \frac{4 x ^{3}}{3} + C

Solution steps

\int - 4 x^{\frac{3}{2}} + 3 x^{\frac{2}{3}} - 4 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 4 x^{\frac{3}{2}} d x + \int 3 x^{\frac{2}{3}} d x - \int 4 x^{2} d x

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

\int 3 x^{\frac{2}{3}} d x = \frac{9}{5} x^{\frac{5}{3}}

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

= - \frac{8}{5} x^{\frac{5}{2}} + \frac{9}{5} x^{\frac{5}{3}} - \frac{4 x ^{3}}{3}

Add a constant to the solution

= - \frac{8}{5} x^{\frac{5}{2}} + \frac{9}{5} x^{\frac{5}{3}} - \frac{4 x ^{3}}{3} + C

What is the integral of-4x^{3/2}+3x^{2/3}-4x^2 ?
The integral of-4x^{3/2}+3x^{2/3}-4x^2 is -8/5 x^{5/2}+9/5 x^{5/3}-(4x^3)/3+C