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

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

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integral of x^5+5sqrt(x)

\int x^{5} + 5 x d x

\frac{x ^{6}}{6} + \frac{10}{3} x^{\frac{3}{2}} + C

Solution steps

\int x^{5} + 5 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 x^{5} d x + \int 5 x d x

\int x^{5} d x = \frac{x ^{6}}{6}

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

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

Add a constant to the solution

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

\int (5 x^{3} + 2)^{2} d x

\int (a x + b)^{2} d x

\int 10 x (ln (x))^{2} d x

\int (5 x^{2} + 6)^{2} d x

\int (x^{3} + 1)^{10} d x

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