`int_3^10[log[x]]dx`

Show that : int_0^1(logx)/((1+x))dx=-int_0^1(log(1+x))/x dx

Evaluate int x^(2) log x dx

Prove that int_(0)^(1)log((x)/(x-1))dx=int_(0)^(1)log((x-1)/(x))dx . Find the value of int_(0)^(1)log((x)/(x-1))dx

Show that int_(0)^(1)log((1-x)/(x))dx=0

Evaluate: int_1^a xdota^(-[(log)_a x])dx ,(a >1)dot

Evaluate the following integrals using properties of integration : int_(0)^(1)(log(1+x))/(1+x^2)dx .

Integrate the following with respect to x. (i) int(2x + 4)/(x^2 + 4x + 6) dx " " (ii) int (e^x)/(e^x - 1) dx " " (iii) int 1/(x log x) dx (iv) int(sin x + cos x)/(sin x - cos x) dx " " (v) int (cos 2x)/((sin x + cos x)^2) dx .

Evaluate int_(-1)^(1)log((3-x)/(3+x))dx .

Evaluate: int x log x dx .

Evaluate the followig integrals (i) int xe^x dx " " (ii) int x cos x dx " " (iii) int log x dx " " (iv) int sin^(-1)x dx .