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(1)/(sqrt(x+a)-sqrt(x+b))+x^(2)sin(x^(3)...

(1)/(sqrt(x+a)-sqrt(x+b))+x^(2)sin(x^(3))

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intsqrt(x/(1-x))\ dx is equal to (a) sin^(-1)sqrt(x)+C (b) sin^(-1){sqrt(x)-sqrt(x(1-x))}+C (c) sin^(-1){sqrt(x(1-x))}+C (d) sin^(-1)sqrt(x)-sqrt(x(1-x))+C

int sqrt((x)/(1-x))dx is equal to sin^(-1)sqrt(x)+C(b)sin^(-1){sqrt(x)-sqrt(x(1-x))}+C(c)sin^(-1){sqrt(x(1-x)}+C(d))sin^(-1)sqrt(x)-sqrt(x(1-x))+C

f(x)=((1)/(sqrt(b-a)))(((sqrt((b-a)/(a)))sin2x)/(sqrt(1+(((sqrt(b-a))/(a)))sin x)))(sqrt(a+b tan^(2)x) at x=3(pi)/(4)(sqrt(a+b tan^(2)x)

f(x)=((1)/(sqrt(b-a)))(((sqrt((b-a)/(a)))sin2x)/(sqrt(1+(((sqrt(b-a))/(a)))sin x)))(sqrt(a+b tan^(2)x) at x=3(pi)/(4)(sqrt(a+b tan^(2)x)

Applying logrithmic differentiation find the derivatives of the following functions (a) y=(cos x)^(sin x) (b) y=((3 sqrt(sin 3x))/(1-sin 3x)) (c ) y=sqrt(x-1)/((3sqrt(x+2))^(2)(sqrt(x+3))^(3))

int_(0)^(1)sin^(-1)(x sqrt(1-x)-sqrt(x)sqrt(1-x^(2)))dx

(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x)),x in[0,1]

(1)/(sqrt(x)+sqrt(x+1))+(1)/(sqrt(x+1)+sqrt(x+2))+(1)/(sqrt(x+2)+sqrt(x+3))+...(1)/(sqrt(x+98)+sqrt(x+99))

(d)/(dx)[sin^(-1)(x sqrt(1-x)-sqrt(x)sqrt(1-x^(2)))] is

sin^(-1)[x sqrt(1-x)-sqrt(x)sqrt(1-x^(2))]=