The integral of (x^2-4secxtanx) dx=

I got x^3/3-4secx+c

Yes, that's right. `u`

To find the integral of the given expression, we can simplify it by expanding and combining like terms:

∫ (x^2 - 4sec(x)tan(x)) dx

First, let's simplify the expression by factoring out any common terms or simplifying any trigonometric identities:

∫ (x^2 - 4sec(x)tan(x)) dx
= ∫ x^2 dx - ∫ 4sec(x)tan(x) dx

Now, we can evaluate each integral separately:

First integral: ∫ x^2 dx
To integrate x^2, we can use the power rule for integration. The power rule states that if we have ∫ x^n dx, where n ≠ -1, the integral is (x^(n+1))/(n+1) + C.

Using the power rule, we find:
∫ x^2 dx = (x^(2+1))/(2+1) + C
= (x^3)/3 + C

Second integral: ∫ 4sec(x)tan(x) dx
To integrate sec(x)tan(x), we can use the substitution method. Let u = sec(x) + tan(x), then du = (sec(x)tan(x) + sec^2(x)) dx.

Now, we can rewrite the integral as:
∫ 4sec(x)tan(x) dx = ∫ du

Integrating du gives us:
∫ du = u + C
= sec(x) + tan(x) + C

Finally, combining the results of both integrals, we have:
∫ (x^2 - 4sec(x)tan(x)) dx = (x^3)/3 + sec(x) + tan(x) + C

Therefore, the correct result is (x^3/3) + sec(x) + tan(x) + C, where C is the constant of integration.