What is the integral of sqrt(2x+6) ?

The integral of sqrt(2x+6) is 1/3 (2x+6)^{3/2}+C

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integral of sqrt(2x+6)

\int 2 x + 6 d x

\frac{1}{3} (2 x + 6)^{\frac{3}{2}} + C

Solution steps

\int 2 x + 6 d x

Apply u-substitution

: \int \frac{u}{2} d u

= \int \frac{u}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int u d u

Apply the Power Rule

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

= \frac{1}{2} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 2 x + 6

= \frac{1}{2} \cdot \frac{2}{3} (2 x + 6)^{\frac{3}{2}}

Simplify

\frac{1}{2} \cdot \frac{2}{3} (2 x + 6)^{\frac{3}{2}} : \frac{1}{3} (2 x + 6)^{\frac{3}{2}}

= \frac{1}{3} (2 x + 6)^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{3} (2 x + 6)^{\frac{3}{2}} + C

\frac{1}{4 ( 1 + x ^{2} )}, \frac{1}{8} x^{2}

n = 0 \sum \infty e^{- 8 n}

(1 - x)^{3} - lo g_{e} (1 - x)

\frac{5 x ^{2}}{3 x - 1}

\int_{1}^{2} 3 - \frac{6}{x ^{2}} d x

What is the integral of sqrt(2x+6) ?
The integral of sqrt(2x+6) is 1/3 (2x+6)^{3/2}+C