Question

Integrate 3√x⁴

Answer 1

wrong again.
3√(x^4) can mean either
3*√(x^4) = 3x^2, which is boring
or
x^(3/4)
But you have interpreted it as 3*x^(3/4)

I suspect the user meant ∛x^4, as otherwise the problem is not very interesting. So that means our solution is
∫∛x^4 dx = ∫x^(4/3) dx = 3/7 x^(7/3) + C

Answer 2

To integrate 3√(x^4), we can use the power rule for integration.

The power rule states that ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration.

Using this rule, we can integrate 3√(x^4) as:

∫3√(x^4) dx

= 3∫(x^4)^(1/3) dx

= 3 ∫(x^(4/3)) dx

Using the power rule, we can integrate x^(4/3) as:

= 3 * (x^(4/3 + 1))/(4/3 + 1) + C

= 3 * (x^(7/3))/(7/3) + C

Simplifying further, we have:

= 9/7 * x^(7/3) + C

Therefore, the integral of 3√(x^4) is (9/7) * x^(7/3) + C.

Answer 3

You are correct, my apologies for the mistake. The correct interpretation of 3√(x^4) is indeed ∛x^4.

Therefore, the integral of ∛x^4 is ∫x^(4/3) dx, which can be evaluated using the power rule.

Using the power rule, we have:

∫x^(4/3) dx = (3/7) * x^(7/3) + C

Thus, the correct solution is (3/7) * x^(7/3) + C. Thank you for pointing out the error.