`int((x^2+1))/((x+1)^2)dxi se q u a lto` `((x-1)/(x+1))e^x+c` (b) `e^x((x+1)/(x-1))+c` `e^x(x+1)(x-1)+c` (d) none of these

int sin^(-1)((2x)/(1+x^(2)))dx is e q u a lto

(xe^x)/(1+x)^2dx= (A) e^x/(1+x) (B) e^x/(1+x)^2 (C) e^xlog(1+x) (D) none of these

The integral inte^x(f(x)+f\'(x))dx can be solved by using integration by parts such that: I=inte^xf(x)dx+inte^xf\'(x)dx=e^xf(x)-inte^xf\'(x)dx+inte^xf\'(x)dx=e^xf(x)+C , and inte^(ax)(f(x)+(f\'(x))/a)dx=e^(ax)f(x)/a+C ,Now answer the question: int(e^x(2-x^2))/((1-x)sqrt(1-x^2))dx (A) e^xsqrt((1-x)/(1+x))+C (B) e^xsqrt((1+x)/(1-x))+C (C) e^xsqrt((2-x)/(2+x))+C (D) none of these

int((ln(tan x))/(sin x cos x)dxi se q u a lto (a) (1)/(2)ln(tan x)+c(b)(1)/(2)ln(tan^(2)x)+c(c)(1)/(2)(ln(tan x))^(2)+c(d) none of these

int e^(x)((x-2)/((x-1)^(2)))dx is equal to (i) (e^(x))/(x-1)+C (ii) (e^(x))/((x-1)^(2))+C( iii) (2e^(x))/((x-1)^(2))+C( iv )(e^(x)-1)/(x-1)+C

The maximum value of x^((1)/(z)),x>0 is (a) e^((1)/(e))(b)((1)/(e))^(e)(c)1(d) none of these

For int (x -1)/( (x +1 ) ^(3)) e ^(x) dx = e ^(x) f (x) + c , f (x) =(x +1) ^(2).

int(1)/(1+e^(x))dx= (a) log(1+e^(x)) (b) log((1+e^(x))/(e^(x))) (c) log(1+e^(-x)) (d) -log(e^(-x)+1)

(d)/(dx){sin^(-1)(e^(x))} is equal to (a) e^(x)sin^(-1)(e^(x)) (b) (e^(x))/(sqrt(1-e^(2x))) (c) (e^(x))/(1-e^(x)) (d) e^(x)cos^(-1)x]]

int(1)/(x^(2))e^((x-1)/(x))=......," (A) "(x)/(e^(x-1))+c," (B) "e^((x-1)/(x))+c," (C) "-e^((x)/(x-1))+c," (D) "-e^((x-1)/(x))+c