The value of `int(a x^2)/(xsqrt(c^2x^2-(a x^2+b)^2))` `1/csin^(-1)(a x+b/x)+k` `csin^(-1)(a+b/x)+e` `sin^(-1)((a x+b/x)/c)+k` (d) none of these

The value of int(a x^2-b)/(xsqrt(c^2x^2-(a x^2+b)^2)) (a) 1/csin^(-1)(a x+b/x)+k (b) csin^(-1)(a+b/x)+e (c) sin^(-1)((a x+b/x)/c)+k (d) none of these

The value of int(a x^2-b)/(xsqrt(c^2x^2-(a x^2+b)^2)) (a) 1/csin^(-1)(a x+b/x)+k (b) csin^(-1)(a+b/x)+e (c) sin^(-1)((a x+b/x)/c)+k (d) none of these

The value of int(ax^(2))/(x sqrt(c^(2)x^(2)-(ax^(2)+b)^(2)))(1)/(c)sin^(-1)(ax+(b)/(x))+k csin^(-1)(a+(b)/(x))+esin^(-1)((ax+(b)/(x))/(c))+k( d) none of these

The antiderivative of (2^x)/(sqrt(1-4^x)) w.r.t x is (A) (log)_2edotsin^(-1)(2^x)+k (B) ""sin^(-1)(2^x)+k (C) ""cos^(-1)(2^x)dot1/((log)_e2)+k (D) none of these

If a (A) x=0 (B) x=1 (C) x=2 (D) None of these.

int e^x((x^2+1))/((x+1)^2)dx is equal to ((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

The value of x which satisfies sin^(-1)(1-x)-2sin^(-1)x=(pi)/(2) is (A) x=1 (B) x=(1)/(2)(C)x=0 (D) none of these

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

The minimum value of e^((2x^(2)-2x+1)sin^(2)x) is e(b)(1)/(e)(c)1(d)0

The minimum value of e^((2x^(2) - 2x + 1) sin^(2) x) is a)e b) 1//e c)1 d)0