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

y = \frac{5 x}{x + 2}, (3, 3)

\frac{\partial}{\partial x} (1 (x - y) e^{y + 2 x^{2}})

y + y^{^{''}} = 0

x \to 0 + lim (\frac{x}{x + ∣ x ∣})

\frac{\partial}{\partial x} (z^{3} - 3 x yz)

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