Solving integrals with the table of integrals

[Jgoshorn1]

Homework Statement

∫e^2xarctan(e^x)dx

Homework Equations

From the table of integrals:
#92 ∫utan^-1udu = (u²+1)/2)tan^-1-u/2 + c

or

#95 ∫uⁿtan^-1udu = 1/(n+1)[uⁿ⁺¹tan^-1-∫ (uⁿ⁺¹du)/(1+u²) , n≠-1

The Attempt at a Solution

The answer is 1/2(e^2x+1)arctan(e^x) - (1/2)e^x + C

I don't know if I'm supposed to make a substitution first and if so what I should substitute and/or if which from I should use from the table. I've tried to make the initial substitution of e^2x and e^x and they both got me seemingly nowhere. Help please.

 

[LCKurtz]

Homework Statement

∫e^2xarctan(e^x)dx

Homework Equations

From the table of integrals:
#92 ∫utan^-1udu = (u²+1)/2)tan^-1-u/2 + c

or

#95 ∫uⁿtan^-1udu = 1/(n+1)[uⁿ⁺¹tan^-1-∫ (uⁿ⁺¹du)/(1+u²) , n≠-1

The Attempt at a Solution

The answer is 1/2(e^2x+1)arctan(e^x) - (1/2)e^x + C

I don't know if I'm supposed to make a substitution first and if so what I should substitute and/or if which from I should use from the table. I've tried to make the initial substitution of e^2x and e^x and they both got me seemingly nowhere. Help please.

Try ##u=e^x## and see if you can't get it in a form to use 95 with ##u^n## in front for some ##n##.