What is the integral of sqrt(2x+3) ?

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

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integral of sqrt(2x+3)

\int 2 x + 3 d x

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

Solution steps

\int 2 x + 3 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 + 3

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

Simplify

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

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

Add a constant to the solution

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

\frac{d}{d x} (5 - 6 x)

\int x (x + 3) d x

\frac{d}{d x} (3 x^{2} - 27)

n = 1 \sum \infty \frac{1}{( 2 n - 1 ) ^{6}}

\int_{0}^{l n (3)} e^{2 x} d x

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