What is the integral of 5x^{3/2}+2sqrt(x) ?

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

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integral of 5x^{3/2}+2sqrt(x)

\int 5 x^{\frac{3}{2}} + 2 x d x

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

Solution steps

\int 5 x^{\frac{3}{2}} + 2 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 5 x^{\frac{3}{2}} d x + \int 2 x d x

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

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

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

Add a constant to the solution

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

\int (1 - 2 x^{2} - \frac{4}{x ^{- 3}}) x^{- 3} d x

\int (7 x^{2} - 12 x) e^{2 x} d x

x \to - 2 - lim (- 3 x^{2} + 2)

y^{^{'}} = \frac{1}{2} + \frac{1}{4} sin (t) - \frac{y}{50}

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