What is the integral of sqrt(5x+1) ?

The integral of sqrt(5x+1) is 2/15 (5x+1)^{3/2}+C

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integral of sqrt(5x+1)

\int 5 x + 1 d x

\frac{2}{15} (5 x + 1)^{\frac{3}{2}} + C

Solution steps

\int 5 x + 1 d x

Apply u-substitution

: \int \frac{u}{5} d u

= \int \frac{u}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int u d u

Apply the Power Rule

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

= \frac{1}{5} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 5 x + 1

= \frac{1}{5} \cdot \frac{2}{3} (5 x + 1)^{\frac{3}{2}}

Simplify

\frac{1}{5} \cdot \frac{2}{3} (5 x + 1)^{\frac{3}{2}} : \frac{2}{15} (5 x + 1)^{\frac{3}{2}}

= \frac{2}{15} (5 x + 1)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{15} (5 x + 1)^{\frac{3}{2}} + C

\frac{s}{( s ^{2} + 25 ) ^{2}}

\int 3 x (5 - x) d x

x \to 0 lim (\frac{x}{2 tan ( x )})

\frac{d}{d x} (\frac{x ^{3}}{6})

\int_{0}^{1} \frac{1}{5 x - 3} d x

What is the integral of sqrt(5x+1) ?
The integral of sqrt(5x+1) is 2/15 (5x+1)^{3/2}+C