Let `a=int_0^(log2) (2e^(3x)+e^(2x)-1)/(e^(3x)+e^(2x)-e^x+1)dx`, then `4e^a`=

int_(0)^(log 2)(e^(x))/(1+e^(x))dx=

int_0^1 x^2 e^(2x) dx

int (e^x)/e^(2x-4) dx

int_(0)^(1)e^(2x)e^(e^(x) dx =)

int (e^(x)dx)/(e^(2x)+4e^(x)+3)

Evaluate int_(log1//3)^(log3)tan((e^(x)-1)/(e^(x)+1))dx

int1/(1+3e^x+2e^(2x))dx

If I=int(e^x)/(e^(4x)+e^(2x)+1) dx. J=int(e^(-x))/(e^(-4x)+e^(-2x)+1) dx. Then for an arbitrary constant c, the value of J-I equal to

int(e^x)/((1+e^x)(2+e^x))dx

If int_(0)^(1) x e^(x^(2) ) dx=alpha int_(0)^(1) e^(x^(2)) dx , then