What is the integral of sqrt(4x+2) ?

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

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integral of sqrt(4x+2)

\int 4 x + 2 d x

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

Solution steps

\int 4 x + 2 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 + 2

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

Simplify

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

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

Add a constant to the solution

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

\int_{0}^{π} sin^{3} (x co) s^{2} x

\int (tan (5 x) + sec (5 x))^{2} d x

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

\frac{1}{x ^{3}}

\int_{0}^{2} - 5 x^{3} x^{2} + 4 d x

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