What is the integral of sqrt(x)(6+5x) ?

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

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integral of sqrt(x)(6+5x)

\int x (6 + 5 x) d x

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

Solution steps

\int x (6 + 5 x) d x

Expand

x (6 + 5 x) : 6 x + 5 x^{\frac{3}{2}}

= \int 6 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 6 x d x + \int 5 x^{\frac{3}{2}} d x

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

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

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

Add a constant to the solution

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

\frac{4}{( x )}

\int_{0}^{0.6} ln (sec (x)) d x

\frac{d ^{2}}{d x ^{2}} (6 x + 11)

x \to 4 + lim (\frac{x - 5}{x - 4})

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

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