What is the integral of (2x+1)^{5/6} ?

The integral of (2x+1)^{5/6} is 3/11 (2x+1)^{11/6}+C

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integral of (2x+1)^{5/6}

\int (2 x + 1)^{\frac{5}{6}} d x

\frac{3}{11} (2 x + 1)^{\frac{11}{6}} + C

Solution steps

\int (2 x + 1)^{\frac{5}{6}} d x

Apply u-substitution

: \int \frac{u ^{\frac{5}{6}}}{2} d u

= \int \frac{u ^{\frac{5}{6}}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int u^{\frac{5}{6}} d u

Apply the Power Rule

: \frac{6}{11} u^{\frac{11}{6}}

= \frac{1}{2} \cdot \frac{6}{11} u^{\frac{11}{6}}

Substitute back

u = 2 x + 1

= \frac{1}{2} \cdot \frac{6}{11} (2 x + 1)^{\frac{11}{6}}

Simplify

\frac{1}{2} \cdot \frac{6}{11} (2 x + 1)^{\frac{11}{6}} : \frac{3}{11} (2 x + 1)^{\frac{11}{6}}

= \frac{3}{11} (2 x + 1)^{\frac{11}{6}}

Add a constant to the solution

= \frac{3}{11} (2 x + 1)^{\frac{11}{6}} + C

\frac{\partial}{\partial x} (32 x + 13 y + 90)

\frac{d}{d t} (ln (a + v (t) t))

\frac{d}{d x} ((- 1)^{n} x^{2 n})

y^{^{'}} = 0.5 y, y (2) = 100

x \to - 1 lim (\frac{∣ x + 1 ∣}{x + 1})

What is the integral of (2x+1)^{5/6} ?
The integral of (2x+1)^{5/6} is 3/11 (2x+1)^{11/6}+C