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

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

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integral of sqrt(x+5)

\int x + 5 d x

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

Solution steps

\int x + 5 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 + 5

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

Add a constant to the solution

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

sec^{2} (π t)

(1, - 6), (4, - 6)

\int (x^{4} + \frac{16}{4 x})^{2} d x

- x^{2} + 2 x + a

x \to c lim (15)

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