# How do you find the antiderivative of f(x)= x^(3/4) + x^(4/3)?

Mar 6, 2018

$\frac{4}{7} {x}^{\frac{7}{4}} + \frac{3}{7} {x}^{\frac{7}{3}} + c$

#### Explanation:

$\text{integrate each term using the "color(blue)"power rule}$

•color(white)(x)int(ax^n)dx=a/(n+1)x^(n+1)

$\Rightarrow \int \left({x}^{\frac{3}{4}} + {x}^{\frac{4}{3}}\right) \mathrm{dx}$

$= \frac{1}{\frac{7}{4}} {x}^{\frac{7}{4}} + \frac{1}{\frac{7}{3}} {x}^{\frac{7}{3}} + c$

$= \frac{4}{7} {x}^{\frac{7}{4}} + \frac{3}{7} {x}^{\frac{7}{3}} + c$

$\text{where c is the constant of integration}$