# CALC

posted by .

Evaluate the integral: the integral of [5e^(2t)]/[1+4e^(2t)]dt. I used u sub and let u=e^2t and got 5/2arctan(e^2t)+C. But this answer is incorrect. Please help. Thanks

• CALC -

There are certain pattern that you should recognize in derivatives

e.g. if y = ln(anything)
then dy/dx = derivative(anything)/anything

I noticed that the derivative of the denominator appears at the top, differing only in a constant

y = ln(1 + 4e^(2t))
dy/dt = 8e^(2t)/(1 + 4e^(2t) )

instead of the 5 I need on top I see an 8

y = (5/8)ln(1 + 4e^(2t) ) + C

## Similar Questions

1. ### calc

how do you start this problem: integral of xe^(-2x) There are two ways: 1) Integration by parts. 2) Differentiation w.r.t. a suitably chosen parameter. Lets do 1) first. This is the "standard method", but it is often more tedious than …
2. ### calc asap!

can you help me get started on this integral by parts?
3. ### CALC

Evaluate The integral from 0 to 5 of (t)(e^-t)dt. I got -5e^-5+-e^-5, but this is incorrect.
4. ### Calculus

Evaluate the integral: the integral of [5e^(2t)]/[1+4e^(2t)]dt. I used u sub and let u=e^2t and got 5/2arctan(e^2t)+C. But this answer is incorrect. Please help. Thanks
5. ### Calculus

Evaluate the integral: the integral of [5e^(2t)]/[1+4e^(2t)]dt. I used u sub and let u=e^2t and got 5/2arctan(e^2t)+C. But this answer is incorrect. Please help. Thanks
6. ### calc

find integral using table of integrals ) integral sin^4xdx this the formula i used integral sin^n xdx =-1/n sin^n-1xcosx +n-1/n integral sin^n-2 using the formula this is what i got: integral sin^4xdx=-1/4sin^3xcosx+3/4 integral sin^2xdx= …
7. ### Calculus 2

The question is: Evaluate the improper integral for a>0. The integral is: the integral from 0 to infinity, of e^(-y/a)dy Can anyone help me solve this?
8. ### Calc

Evaluate the integral using any method: (Integral)sec^3x/tanx dx I started it out and got secx(1tan^2x)/tanx. I know I just have to continue simplifying and finding the integral, but I'm stuck on the next couple of steps. Also, I have …
9. ### Calculus integral

evaluate the integral: integral from -pi/4 to 0 for the function 6sec^3x dx. it has to be an exact answer and i did it and keep getting it wrong. I got 4sqrt(2)-4ln(-sqrt(2)+1)
10. ### Calc

Use the table of integral to evaluate: the integral of x^4 sinxdx. Please indicate the number of formula used.

More Similar Questions