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

The integral of x(x+1)^{1/3} is 3/4 x(x+1)^{4/3}-9/28 (x+1)^{7/3}+C

Popular >

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

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

\frac{3}{4} x (x + 1)^{\frac{4}{3}} - \frac{9}{28} (x + 1)^{\frac{7}{3}} + C

Solution steps

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

Apply Integration By Parts

: \frac{3}{4} x (x + 1)^{\frac{4}{3}} - \int \frac{3}{4} (x + 1)^{\frac{4}{3}} d x

= \frac{3}{4} x (x + 1)^{\frac{4}{3}} - \int \frac{3}{4} (x + 1)^{\frac{4}{3}} d x

\int \frac{3}{4} (x + 1)^{\frac{4}{3}} d x = \frac{9}{28} (x + 1)^{\frac{7}{3}}

= \frac{3}{4} x (x + 1)^{\frac{4}{3}} - \frac{9}{28} (x + 1)^{\frac{7}{3}}

Add a constant to the solution

= \frac{3}{4} x (x + 1)^{\frac{4}{3}} - \frac{9}{28} (x + 1)^{\frac{7}{3}} + C

\int \frac{1}{4 + 49 x ^{2}} d x

\int \frac{e ^{x}}{e ^{2 x}} d x

\int \frac{1}{( x ^{2} - 6 x + 10 ) ^{\frac{5}{2}}} d x

\int \frac{cos ( 2 x )}{sin ^{2} ( x )} d x

\int \frac{sin ( x )}{sin ^{3} ( x ) + cos ^{3} ( x )} d x

What is the integral of x(x+1)^{1/3} ?
The integral of x(x+1)^{1/3} is 3/4 x(x+1)^{4/3}-9/28 (x+1)^{7/3}+C