Question

Calculas help?
∫??(5−ex)(e2x)dx

Answer 1

\[\int\limits_{?}^{?}(5-e ^{x})(e ^{2x})\]

Answer 2

Multiply it out, it's gonna make your life much easier

Answer 3

Int (5e^(2x)-e^(3x),x)

Answer 4

opps it is suppose to be divided by the second e

Answer 5

ohh that makes it a little different

Answer 6

yea i would think so lol

Answer 7

oh still rewrite it as:
Int (5/e^(2x) - e^x/e^(2x)))
Int (5*e^(-2x) - e^(-x))

Answer 8

Now split it into two:
5 * Int(e^(-2x)) - Int(e^(-x))

Answer 9

Now just use the rule:
Int (e^(kx)) = e^(kx) / k

Answer 10

In the first half k = -2, in the second half, k = -1
So finally:
5 * (e^(-2x)/(-2)) + e^(-x) + C

Answer 11

ok that makes sense thanks

Answer 12

btw to prove that Int (e^(kx)) = e^(kx)/k just use u sub. Let u = kx, du = k dx, etc..