What is the integral of (700x)/((x+1)^{1/3)} ?

The integral of (700x)/((x+1)^{1/3)} is 700(3/2 x(x+1)^{2/3}-9/10 (x+1)^{5/3})+C

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integral of (700x)/((x+1)^{1/3)}

\int \frac{700 x}{( x + 1 ) ^{\frac{1}{3}}} d x

700 (\frac{3}{2} x (x + 1)^{\frac{2}{3}} - \frac{9}{10} (x + 1)^{\frac{5}{3}}) + C

Solution steps

\int \frac{700 x}{( x + 1 ) ^{\frac{1}{3}}} d x

Take the constant out:

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

= 700 \cdot \int \frac{x}{( x + 1 ) ^{\frac{1}{3}}} d x

Apply Integration By Parts

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

= 700 (\frac{3}{2} x (x + 1)^{\frac{2}{3}} - \int \frac{3}{2} (x + 1)^{\frac{2}{3}} d x)

\int \frac{3}{2} (x + 1)^{\frac{2}{3}} d x = \frac{9}{10} (x + 1)^{\frac{5}{3}}

= 700 (\frac{3}{2} x (x + 1)^{\frac{2}{3}} - \frac{9}{10} (x + 1)^{\frac{5}{3}})

Add a constant to the solution

= 700 (\frac{3}{2} x (x + 1)^{\frac{2}{3}} - \frac{9}{10} (x + 1)^{\frac{5}{3}}) + C

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What is the integral of (700x)/((x+1)^{1/3)} ?
The integral of (700x)/((x+1)^{1/3)} is 700(3/2 x(x+1)^{2/3}-9/10 (x+1)^{5/3})+C