1. ## antiderivative help

a little confused on this one. more advanced than the ones we've done in class. any step by step help is appreciated.

NOTE: i'm not too sure why it's not letting me enter x to the 10th power or 2x to the -1 power. thats why it looks weird but it's supposed to be x^10 and 2x^-1

find the anti-derivative:

$\displaystyle f(x) = x^10 + \sqrt{x^3} + \frac{1}{\sqrt[7]{x}} +2x^-1$

2. Put the exponent in curly braces, like x^{10}.

Write it as $\displaystyle x^{10}+x^{3/2}+x^{-1/7}+2x^{-1}$ and use the rules $\displaystyle \int x^\alpha = \frac1{\alpha+1}x^{\alpha+1}$ for $\displaystyle \alpha\neq-1$ and $\displaystyle \int\frac1x = \log|x|$ otherwise.

3. Originally Posted by JGaraffa
a little confused on this one. more advanced than the ones we've done in class. any step by step help is appreciated.

NOTE: i'm not too sure why it's not letting me enter x to the 10th power or 2x to the -1 power. thats why it looks weird but it's supposed to be x^10 and 2x^-1

find the anti-derivative:

$\displaystyle f(x) = x^10 + \sqrt{x^3} + \frac{1}{\sqrt[7]{x}} +2x^-1$
Remember $\displaystyle \sqrt(x) = x^{1/2} and \sqrt[7]{x} = x^{1/7} and \int{\frac{2}{x}} = 2\int{\frac{1}{x}}$

Using you're basic Anti-derivatives rules.

$\displaystyle \frac{x^{11}}{11} + \frac{2x^{5/2}}{5} + \frac{7x^{6/7}}{6} +2\ln{x}$