Question

find

∫ (3^x - 5)(4^x + 7) dx

Answer 1

first, just expand the product to get

∫ 12^x - 5*4^x + 7*3^x - 35 dx
Now recall that since
d/dx a^x = lna * a^x
∫ a^x dx = 1/lna * a^x
That gives you a final result of
1/ln12 * 12^x - 5/ln4 * 4^x + 7/ln3 * 3^x - 35x + C