## anonymous 4 years ago Calculas help? ∫??(5−ex)(e2x)dx

1. anonymous

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

2. bahrom7893

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

3. bahrom7893

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

4. anonymous

opps it is suppose to be divided by the second e

5. bahrom7893

ohh that makes it a little different

6. anonymous

yea i would think so lol

7. bahrom7893

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

8. bahrom7893

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

9. bahrom7893

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

10. bahrom7893

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

11. anonymous

ok that makes sense thanks

12. bahrom7893

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