Question

How do I find the indefinite integral of the attached problem?

Answer 1

power rule

Answer 2

Just use the power rule for integration. Don't be afraid to apply it to rational exponents as well :)

Answer 3

\[\huge \int \sqrt[5]{x^3}dx \implies \int x^{3/5} dx\]

Answer 4

Trick. Rewrite it as
\[\Large \int\limits x^\frac{3}{5}\]

Answer 5

they get larger and larger

Answer 6

\[\LARGE \int u^n du \implies \frac{u^{n+1}}{n+1}\]

Answer 7

\[\small \int x^{\frac{3}{5}}dx\]

Answer 8

\[\tiny \int x^{\frac{3}{5}}dx\]

Answer 9

I did that, and it keeps saying it's wrong.

Answer 10

did you make sure to write the stupid +C ?

Answer 11

This is a sample problem:

Answer 12

yeah, looks good

Answer 13

Yes, it's still wrong even after I put the C.

Answer 14

\[\frac{3}{5}+1=\frac{8}{3}\] you get
\[\frac{3}{8}x^{\frac{8}{3}}+C\]

Answer 15

is that what you put?

Answer 16

No

Answer 17

Hey hey, girl.
How's yo' day, girl?
I'm sorry to confuse ya'
let me put it this way, girl.

SO, if the integral is simply a power of x, something like x^2, x^4, x^(4/7) etc, then we have a simple rule for how to integrate it. This problem isn't like that, BUT we can rewrite it so that it's like that, a power of x. That's the first step. We'll rewrite the exponent as a fraction and put the power in the numerator and the root in the denominator.
\[\huge \int\limits \sqrt[5]{x^3} = \int\limits x^\frac{3}{5}\]

Answer 18

So that's step one. Now that it's simply a power of x, we can use our simple rule.
What is our simple rule for powers of x? Well, it's the opposite of what our power rule was when we did derivatives.
With derivatives, you'll remember that it was to MULTIPLY the coefficient by the power and then to SUBTRACT one from the power.
With integrals we ADD one to the power, then we DIVIDE the coefficient by that new power.

What is 3/5 + 1?