What is the integral of sqrt(x)(6+10x) ?

The integral of sqrt(x)(6+10x) is 4x^{3/2}+4x^{5/2}+C

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integral of sqrt(x)(6+10x)

\int x (6 + 10 x) d x

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

Solution steps

\int x (6 + 10 x) d x

Expand

x (6 + 10 x) : 6 x + 10 x^{\frac{3}{2}}

= \int 6 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 6 x d x + \int 10 x^{\frac{3}{2}} d x

\int 6 x d x = 4 x^{\frac{3}{2}}

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

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

Add a constant to the solution

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

\int 13 sec^{- 2} (x t a) n^{3} x d x

y^{^{''}} + y^{^{'}} + y = 0.5

f^{^{'}} (x) = 5

\frac{d}{d x} (\frac{( e ^{x} )}{ln ( x )})

cos (x), at x = \frac{π}{2}

What is the integral of sqrt(x)(6+10x) ?
The integral of sqrt(x)(6+10x) is 4x^{3/2}+4x^{5/2}+C