What is the integral of sqrt(3x+7) ?

The integral of sqrt(3x+7) is 2/9 (3x+7)^{3/2}+C

Popular >

integral of sqrt(3x+7)

\int 3 x + 7 d x

\frac{2}{9} (3 x + 7)^{\frac{3}{2}} + C

Solution steps

\int 3 x + 7 d x

Apply u-substitution

: \int \frac{u}{3} d u

= \int \frac{u}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int u d u

Apply the Power Rule

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

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

Substitute back

u = 3 x + 7

= \frac{1}{3} \cdot \frac{2}{3} (3 x + 7)^{\frac{3}{2}}

Simplify

\frac{1}{3} \cdot \frac{2}{3} (3 x + 7)^{\frac{3}{2}} : \frac{2}{9} (3 x + 7)^{\frac{3}{2}}

= \frac{2}{9} (3 x + 7)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{9} (3 x + 7)^{\frac{3}{2}} + C

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

\int_{0}^{\infty} x e^{- s x} d x

\int tan^{5} (x) sec^{6} (x) d x

(2 x - 2)^{4} (x^{2} + x + 1)^{4}

7 sec^{5} (π t - 8)

What is the integral of sqrt(3x+7) ?
The integral of sqrt(3x+7) is 2/9 (3x+7)^{3/2}+C