What is the integral of 8w^{1/2}-2w^{3/2} ?

The integral of 8w^{1/2}-2w^{3/2} is 16/3 w^{3/2}-4/5 w^{5/2}+C

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integral of 8w^{1/2}-2w^{3/2}

\int 8 w^{\frac{1}{2}} - 2 w^{\frac{3}{2}} d w

\frac{16}{3} w^{\frac{3}{2}} - \frac{4}{5} w^{\frac{5}{2}} + C

Solution steps

\int 8 w^{\frac{1}{2}} - 2 w^{\frac{3}{2}} d w

Apply the Sum Rule:

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

= \int 8 w^{\frac{1}{2}} d w - \int 2 w^{\frac{3}{2}} d w

\int 8 w^{\frac{1}{2}} d w = \frac{16}{3} w^{\frac{3}{2}}

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

= \frac{16}{3} w^{\frac{3}{2}} - \frac{4}{5} w^{\frac{5}{2}}

Add a constant to the solution

= \frac{16}{3} w^{\frac{3}{2}} - \frac{4}{5} w^{\frac{5}{2}} + C

\int \frac{x ^{2} + 5}{x ^{2} + 1} d x

\int 9

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

\int x + e^{- x} d x

\int (\frac{x ^{2}}{1 + x}) d x

What is the integral of 8w^{1/2}-2w^{3/2} ?
The integral of 8w^{1/2}-2w^{3/2} is 16/3 w^{3/2}-4/5 w^{5/2}+C