Question

Find the antiderivative: (x^2)^(1/3) + x(x)^(1/2)

Answer 1

Easier if you simplify the integrand.

Answer 2

rewrite both terms using index laws

\[(x^2)^{\frac{1}{3}} = x^{\frac{2}{3}}\]

and

\[x \times x^{\frac{1}{2}} = x^{\frac{3}{2}}\]

now you can find the antiderivatives

Answer 3

hmm ok thanks

Answer 4

:)

Answer 5

I'm still a bit confused

Answer 6

You can now rewrite it as \[\int\limits_{?}^{?} x^{2/3} + x^{3/2}\]

Answer 7

Yes, so now

Answer 8

I should have something like

Answer 9

dx*

Answer 10

(3/5)x^(5/3) + (2/5)x^(5/2)

Answer 11

?

Answer 12

There ya go.

Answer 13

I took a break from doing this kind of problem and it's still difficult

Answer 14

Don't forget to add C.

Answer 15

Yes? that is it? ? :)))

Answer 16

Yup. See, simplifying the integrand was the trick to the problem.

Answer 17

coool

Answer 18

thanks :)