Having trouble finding the correct substitutions & tricks for this one:
$$\int\limits_{-1}^{1} \frac{7xe^{2x} }{(1 + 2x)^2} dx$$

(don't need to evaluate, will give a medal)

Question

Having trouble finding the correct substitutions & tricks for this one:
$$\int\limits_{-1}^{1} \frac{7xe^{2x} }{(1 + 2x)^2}  dx$$

(don't need to evaluate, will give a medal)

anonymous · Answer

u= (exp(2x))/(1+2x)

anonymous · Answer

amazing, right?  you get just what you want in one step. problem must have been cooked

anonymous · Answer

but be very careful with the integral, because it is improper as the integrand is undefined at $x=-\frac{1}{2}$

anonymous · Answer

very very careful!

anonymous · Answer

Right so it's just a simple u substitution and then splitting the integral up into a sum of two smaller intervals avoiding the -0.5, correct?

anonymous · Answer

u can use this

$$\lim_{t \rightarrow -1/2}(\int\limits\limits_{-1}^{t}f(x)dx+\int\limits\limits_{t}^{1}f(x)dx)$$