`int ((e^(2x)-1))/((e^(2x)+1))dx=`

Evaluate: int(e^(2x)-2e^x)/(e^(2x)+1)dx

Column I, a) int(e^(2x)-1)/(e^(2x)+1)dx is equal to b) int1/((e^x+e^(-x))^2)dx is equal to c) int(e^(-x))/(1+e^x)dx is equal to d) int1/(sqrt(1-e^(2x)))dx is equal to COLUMN II p) x-log[1+sqrt(1-e^(2x)]+c q) log(e^x+1)-x-e^(-x)+c r) log(e^(2x)+1)-x+c s) -1/(2(e^(2x)+1))+c

Evaluate: int(e^(2x))/(e^(2x)-2)dx

(iii) int(e^(x)-1)/(1-e^(-x))dx

(i) int(e^(x))/(1+e^(x))dx" "(ii) int (e^(x)) /((1+e^(x))^(4))dx

Evaluate the following: (i) int(sec^(2)x)/(3+tanx)dx " (ii) " int(e^(x)-e^(-x))/(e^(x)+e^(-x))dx (iii) int(1-tanx)/(1+tanx)dx " (iv) " int(1)/(1+e^(-x))dx

Statement -1 : If I_(1)=int(e^(x))/(e^(4x)+e^(2x)+1)dx and I_(2)=int(e^(-x))/(e^(-4x)+e^(-2x)+1)dx , then I_(2)-I_(1)=(1)/(2)log((e^(2x)-e^(x)+1)/(e^(2x)+e^(x)+1))+C where C is an arbitrary constant. Statement -2 : A primitive of f(x) =(x^(2)-1)/(x^(4)+x^(2)+1) is (1)/(2)log((x^(2)-x+1)/(x^(2)+x+1)) .

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

Evaluate int_(0)^(4)(e^(x))/(1+e^(2x))dx

int(x^(e-1)-e^(x-1))/(x^e-e^x)dx