Question

Find the most general antiderivative of the function.

f(x)=3:sqrt(x^2)+xsqrt(x)

Answer 1

what is the colon for

Answer 2

its the third root.. I wasn't sure how to write that lol

Answer 3

\(\large f(x)=\sqrt[3]{x^2}+x \sqrt x\)

Answer 4

^ exactly.

Answer 5

\[\int\limits\limits_{}^{}\sqrt[3]{x^2}+x \sqrt{x} \space dx\]

Answer 6

\(\huge \int x^ndx= \frac{x^{n+1}}{n+1}+c\)

Answer 7

yes, thank you.

Answer 8

\(\huge \int\limits_{}^{}x^{2 \over 3} + x^{3 \over 2} \space dx\)

Answer 9

right @ChmE ?

Answer 10

\(\huge \sqrt[3]{x^2}= (x^2)^{1/3}=x^{2/3}\)

Answer 11

\(\huge x^1\sqrt x=x^{1+1/2}=x^{3/2}\)

Answer 12

ya you're right @hartnn I did make a mistake. Sorry @monroe17

Answer 13

Just another example of why you should always double check people's responses for yourself and not just take their word for it

Answer 14

Yeah, I got it though. Thanks