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

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

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

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

int(e^(x))/((1+x)^(3))dx-int(e^(x))/(2(1+x)^(2))dx=

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

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

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

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