What is the integral of sqrt(x)(3+10x) ?

The integral of sqrt(x)(3+10x) is 2x^{3/2}+4x^{5/2}+C

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integral of sqrt(x)(3+10x)

\int x (3 + 10 x) d x

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

Solution steps

\int x (3 + 10 x) d x

Expand

x (3 + 10 x) : 3 x + 10 x^{\frac{3}{2}}

= \int 3 x + 10 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 10 x^{\frac{3}{2}} d x

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

\int 10 x^{\frac{3}{2}} d x = 4 x^{\frac{5}{2}}

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

Add a constant to the solution

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

\frac{d ^{2} y}{d x ^{2}} = 4 y

\frac{d v}{d t} = v^{2} + 5 v + 1

\int tan (x) sec^{2} (x) d x

(2 x + 3) (3 x - 4)

\frac{5}{x ^{3}}

What is the integral of sqrt(x)(3+10x) ?
The integral of sqrt(x)(3+10x) is 2x^{3/2}+4x^{5/2}+C