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

The integral of (3x-4/3 x^{3/2}) is (3x^2)/2-8/15 x^{5/2}+C

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integral of (3x-4/3 x^{3/2})

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

\frac{3 x ^{2}}{2} - \frac{8}{15} x^{\frac{5}{2}} + C

Solution steps

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

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

\int \frac{4}{3} x^{\frac{3}{2}} d x = \frac{8}{15} x^{\frac{5}{2}}

= \frac{3 x ^{2}}{2} - \frac{8}{15} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{3 x ^{2}}{2} - \frac{8}{15} x^{\frac{5}{2}} + C

What is the integral of (3x-4/3 x^{3/2}) ?
The integral of (3x-4/3 x^{3/2}) is (3x^2)/2-8/15 x^{5/2}+C