Evaluate the Indefinite Integral

∫(7+tan(x))^12 sec^2(x) dx

you need to use U substitution

say that U=7 + tan(x)
dU=sec^2(x)dx (you take the derivative of U)

so using substitution, the integral is now ∫(U)^12*du

now, integrate. the integral of U^12 is (U^13)/13

now substitute back in what U is equal to... (7+tanx)^13/13

that is your answer

Use simple u-substitution:

∫(7 + tan(x))^(12) * sec²(x) dx

u = 7 + tan(x)

du = sec²(x) dx

∫(u^12) du

= u^13/(13) + C = (7 + tan(x))^(13)/13 + C

Try wolframalpha.com. Type in integrate followed by the problem. It will also show you the steps :)