The first thing we want to do on this problem is split up the denominator so that it's under both of the terms in the numerator. So T the 7th root of T to the 4th over t ^2 DT plus the integral the 7th root of T to the 4th over t ^2 DT. If we change that 7th root of 4 to 4 sevenths and then simplify remembering if the bases are the same, we add the exponents when we're multiplying, and if the bases are the same when we're dividing, we subtract exponents. We get T to the -3 sevenths and T to the -10 sevenths. To find the antiderivative, we find we add 1 to the exponent and divide by the new exponent. So if we add 1 to -3 sevenths, we get 4 sevenths. If we add 1 to -10 sevenths, we get -3 sevenths. Putting it back into the root form, we get 7 the 7th root of T to the 4th over 4 -, 7 / 3 the 7th root of t ^3 + C.