What is the integral of sqrt(x)(3+5x) ?

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

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integral of sqrt(x)(3+5x)

\int x (3 + 5 x) d x

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

Solution steps

\int x (3 + 5 x) d x

Expand

x (3 + 5 x) : 3 x + 5 x^{\frac{3}{2}}

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

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

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

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

Add a constant to the solution

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

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

\frac{2 s ^{2} + 5 s + 5}{( s + 1 ) ^{3}}

(\frac{5}{x}), at x = 4

\int 3 e^{x} + 5 sin (x) d x

y = (x^{3} - 25 x)^{8}, (5, 0)

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