What is the integral of sqrt(x+13) ?

The integral of sqrt(x+13) is 2/3 (x+13)^{3/2}+C

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integral of sqrt(x+13)

\int x + 13 d x

\frac{2}{3} (x + 13)^{\frac{3}{2}} + C

Solution steps

\int x + 13 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 + 13

= \frac{2}{3} (x + 13)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (x + 13)^{\frac{3}{2}} + C

x \to 2 lim (\frac{5 x + 2}{x - 2})

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

y^{^{'}} = y^{2} - 9

\frac{1}{x ^{2} + 1}

\int cos (x) (8 + 4 sin^{2} (x)) d x

What is the integral of sqrt(x+13) ?
The integral of sqrt(x+13) is 2/3 (x+13)^{3/2}+C