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

The integral of (3+2\sqrt[4]{x})^3 is 27x+216/5 x^{5/4}+24x^{3/2}+32/7 x^{7/4}+C

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integral of (3+2\sqrt[4]{x})^3

27 x + \frac{216}{5} x^{\frac{5}{4}} + 24 x^{\frac{3}{2}} + \frac{32}{7} x^{\frac{7}{4}} + 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 27 d x = 27 x

\int 36 x d x = 24 x^{\frac{3}{2}}

\int 8 x^{\frac{3}{4}} d x = \frac{32}{7} x^{\frac{7}{4}}

= 27 x + \frac{216}{5} x^{\frac{5}{4}} + 24 x^{\frac{3}{2}} + \frac{32}{7} x^{\frac{7}{4}}

Add a constant to the solution

= 27 x + \frac{216}{5} x^{\frac{5}{4}} + 24 x^{\frac{3}{2}} + \frac{32}{7} x^{\frac{7}{4}} + C

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

\int e^{x} 33 + e^{x} d x

\int \frac{2 x + 9}{x ^{2} + 9 x + 3} d x

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

\int \frac{2 x - 3}{x ^{2} - 2 x + 5} d x

What is the integral of (3+2\sqrt[4]{x})^3 ?
The integral of (3+2\sqrt[4]{x})^3 is 27x+216/5 x^{5/4}+24x^{3/2}+32/7 x^{7/4}+C