What is the integral of x(1+x)^{2/3} ?

The integral of x(1+x)^{2/3} is 3/5 x(1+x)^{5/3}-9/40 (1+x)^{8/3}+C

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integral of x(1+x)^{2/3}

\int x (1 + x)^{\frac{2}{3}} d x

\frac{3}{5} x (1 + x)^{\frac{5}{3}} - \frac{9}{40} (1 + x)^{\frac{8}{3}} + C

Solution steps

\int x (1 + x)^{\frac{2}{3}} d x

Apply Integration By Parts

: \frac{3}{5} x (1 + x)^{\frac{5}{3}} - \int \frac{3}{5} (1 + x)^{\frac{5}{3}} d x

= \frac{3}{5} x (1 + x)^{\frac{5}{3}} - \int \frac{3}{5} (1 + x)^{\frac{5}{3}} d x

\int \frac{3}{5} (1 + x)^{\frac{5}{3}} d x = \frac{9}{40} (1 + x)^{\frac{8}{3}}

= \frac{3}{5} x (1 + x)^{\frac{5}{3}} - \frac{9}{40} (1 + x)^{\frac{8}{3}}

Add a constant to the solution

= \frac{3}{5} x (1 + x)^{\frac{5}{3}} - \frac{9}{40} (1 + x)^{\frac{8}{3}} + C

y = cos (x), x = \frac{π}{2}, x = 2 π, y = 0

n = 0 \sum \infty \frac{2}{3} (\frac{1}{3})^{n}

\int \frac{7 - x}{x ^{2} - 4 x + 4} d x

\frac{d}{d x} (cos (w x))

x \to - \infty lim (- 3 x - 2)

What is the integral of x(1+x)^{2/3} ?
The integral of x(1+x)^{2/3} is 3/5 x(1+x)^{5/3}-9/40 (1+x)^{8/3}+C