" 5."(1)/(x^(3))(sin log x)

Evaluate: int(1)/(x^(3))sin(log x)dx

If int (1)/(4 + 5 sin x) " dx "= (1)/(3) log |f (x)| + c then f(x) =

1. int(1+x)/(x*sin(x+log x))dx

If f(x)={{:(((5^(x)-1)^(3))/(sin((x)/(a))log(1+(x^(2))/(3)))",",x ne0),(9(log_(e)5)^(3)",",x=0):} is continuous at x=0 , then value of 'a' equals

(i)log(x+(1)/(x))" "(ii)log sin3x" "(iii)log(x+sqrt(1+x^(2)))

Leg f(x)=log(log_(1/3)(log_((1)/(3))(log_(7)(sin x+a)))) be defined for every real value of x, then the possible value of a is 3 (b) 4(c)5(d)6

Prove that lim_(x rarr 0) (log(1+x^3))/(sin^3 x)=1 .

Show that, lim_(x rarr 0) log(1+x^(3))/(sin^(3)x) = 1