What is the integral of sqrt(4x+7) ?

The integral of sqrt(4x+7) is 1/6 (4x+7)^{3/2}+C

Popular >

integral of sqrt(4x+7)

\int 4 x + 7 d x

\frac{1}{6} (4 x + 7)^{\frac{3}{2}} + C

Solution steps

\int 4 x + 7 d x

Apply u-substitution

: \int \frac{u}{4} d u

= \int \frac{u}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int u d u

Apply the Power Rule

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

= \frac{1}{4} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 4 x + 7

= \frac{1}{4} \cdot \frac{2}{3} (4 x + 7)^{\frac{3}{2}}

Simplify

\frac{1}{4} \cdot \frac{2}{3} (4 x + 7)^{\frac{3}{2}} : \frac{1}{6} (4 x + 7)^{\frac{3}{2}}

= \frac{1}{6} (4 x + 7)^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{6} (4 x + 7)^{\frac{3}{2}} + C

\int \frac{x ^{5} + 1}{x} d x

\int \frac{x ^{2} - x}{x} d x

\int x^{(\frac{1}{2})} d x

\int (\frac{3 x ^{2}}{2} + 4)^{2} d x

\int \frac{1}{( x ^{2} + 6 x + 13 ) ^{2}} d x

What is the integral of sqrt(4x+7) ?
The integral of sqrt(4x+7) is 1/6 (4x+7)^{3/2}+C