What is the integral of (\sqrt[3]{2x+1}) ?

The integral of (\sqrt[3]{2x+1}) is 3/8 (2x+1)^{4/3}+C

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integral of (\sqrt[3]{2x+1})

\int (3 2 x + 1) d x

\frac{3}{8} (2 x + 1)^{\frac{4}{3}} + C

Solution steps

\int 3 2 x + 1 d x

Apply u-substitution

: \int \frac{3 u}{2} d u

= \int \frac{3 u}{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 3 u d u

Apply the Power Rule

: \frac{3}{4} u^{\frac{4}{3}}

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

Substitute back

u = 2 x + 1

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

Simplify

\frac{1}{2} \cdot \frac{3}{4} (2 x + 1)^{\frac{4}{3}} : \frac{3}{8} (2 x + 1)^{\frac{4}{3}}

= \frac{3}{8} (2 x + 1)^{\frac{4}{3}}

Add a constant to the solution

= \frac{3}{8} (2 x + 1)^{\frac{4}{3}} + C

h \to + 0 lim (- \frac{5 h}{x ( x + h )})

\frac{d}{d x} (- \frac{3}{1 - 3 x})

\int \frac{6000}{6 x + 70} d x

\int \frac{3}{16 - 9 x ^{2}} d x

y = \frac{x}{x + \frac{b}{x}}

What is the integral of (\sqrt[3]{2x+1}) ?
The integral of (\sqrt[3]{2x+1}) is 3/8 (2x+1)^{4/3}+C