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

The integral of (1-3x+x^3)\sqrt[3]{x} is 3/4 x^{4/3}-9/7 x^{7/3}+3/13 x^{13/3}+C

Popular >

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

\frac{3}{4} x^{\frac{4}{3}} - \frac{9}{7} x^{\frac{7}{3}} + \frac{3}{13} x^{\frac{13}{3}} + C

Solution steps

Expand

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int 3 x^{\frac{4}{3}} d x = \frac{9}{7} x^{\frac{7}{3}}

\int x^{\frac{10}{3}} d x = \frac{3}{13} x^{\frac{13}{3}}

= \frac{3}{4} x^{\frac{4}{3}} - \frac{9}{7} x^{\frac{7}{3}} + \frac{3}{13} x^{\frac{13}{3}}

Add a constant to the solution

= \frac{3}{4} x^{\frac{4}{3}} - \frac{9}{7} x^{\frac{7}{3}} + \frac{3}{13} x^{\frac{13}{3}} + C

\int \frac{1}{4 - ( x - 1 ) ^{2}} d x

\int 10000 - 2 (2 q + q^{3}) d q

\int 20 e^{4 x} d x

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

\int \frac{( 9 - x ^{2} )}{x} d x

What is the integral of (1-3x+x^3)\sqrt[3]{x} ?
The integral of (1-3x+x^3)\sqrt[3]{x} is 3/4 x^{4/3}-9/7 x^{7/3}+3/13 x^{13/3}+C