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.