(16)log((1)/(sqrt(x)))+5x^(a)-3a^(x)+3sqrt(x^(2))+64sqrt(x^(-3))

Differentiate the following with respect of x:log((1)/(sqrt(x)))+5x^(a)-3a^(x)+3sqrt(x^(2))+64backslash sqrt(x)

2sqrt(3)x^(2)-5x+sqrt(3)

lim_(x rarr oo)((sqrt(x^(2)+5)-sqrt(x^(2)-3))/(sqrt(x^(2)+3)-sqrt(x^(2)+1)))

Find the value of x satisfying the equation,sqrt((log_(3)3sqrt(3)x+log_(x)3sqrt(3)x)*log_(3)x^(3))+sqrt(((log_(3)(3sqrt(x)))/(3)+(log_(x)(3sqrt(x)))/(3))*log_(3)x^(3))=2

int ((log(1+6sqrt(x)))/(3sqrt(x)+sqrt(x))+(1)/(3sqrt(x)+4sqrt(x)))dx

f(x)=sqrt(log((3x-x^(2))/(x-1)))

f(x)=sqrt(log((3x-x^(2))/(x-1)))

f(x)=sqrt(log((3x-x^(2))/(x-1)))

If int(x*ln(x+sqrt(1+x^(2))))/(sqrt(1+x^(2)))dx=A*sqrt(1+x^(2))ln(x+sqrt(1+x^(2)))+Bx+c , then (3A^(2)+5B^(2))/(A-B) equal to __________.

int(dx)/(sqrt(3x^(3)+4x+7))=k log|(2x-3)+sqrt(9x^(2)+12x+21)|+c, then k=(i)(1)/(3)(ii)(1)/(sqrt(3))(iit)(2)/(sqrt(3)) (iv) (4)/(sqrt(3))