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

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

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integral of sqrt(x+10)

\int x + 10 d x

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

Solution steps

\int x + 10 d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = x + 10

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

Add a constant to the solution

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

(e^{x} cos (x))^{^{'}}

\int_{0}^{\frac{π}{2}} cos (5 t) cos (10 t) d t

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

x y^{^{'}} - 2 y = \frac{3}{2 x}

\frac{d ^{2}}{d x ^{2}} (sin (3 x^{2} + 2))

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