(6) `int e^(-3) log sqrt(x) dx`

If a >0 and a!=1 evaluate the following integrals: (i) inte^(x\ (log)_e a)\ dx\ (ii) inte^(a\ (log)_e x)\ dx

Evaluate the following integrals: int1/(sqrt(x))\ dx (ii) int1/(x^3)\ dx (iii) inta^(3\ (log)_a x)\ dx

Evaluate: (i) int((1+x)^3)/(sqrt(x))\ dx (ii) int{x^2+e^(logx)+(e/2)^x}\ dx

Evaluate: int cos^(3)x. e^(log sin x)dx

int e^(3sqrt(x))dx

Evaluate : int (e^("log x "))/(x) " dx "

int_(1)^(7)(log sqrt(x))/(log sqrt(8-x)+log sqrt(x))dx=

Evaluate: (i) int(e^x)/(sqrt(4-e^(2x)))\ dx (ii) int(x^2)/(sqrt(1-x^6))\ dx

Evaluate: (i) int(e^x)/(sqrt(4-e^(2x)))\ dx (ii) int(x^2)/(sqrt(1-x^6))\ dx

Evaluate: (i) int(e^x)/(sqrt(4-e^(2x)))\ dx (ii) int(x^2)/(sqrt(1-x^6))\ dx