`int e^(log(1+tan^2x))dx`

int log ( 1 + x^(2)) dx

int e^(x log a ) e^(x) dx is equal to A) (a^(x))/( log ae) + C B) ( e^(x))/( 1+log a ) + C C) ( ae )^(x) +C D) ((ae)^(x))/( log ae) +C

Evaluate int 5^(log _(e)x)dx

int log_(e)(a^(x))dx=

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

If I=inte^(-x)log(e^x+1)dx ,t h e nIe q u a l a+(e^(-x)+1)log(e^x+1)+C a+(e^x+1)log(e^x+1)+C a-(e^(-x)+1)log(e^x+1)+C none of these

STATEMENT-1 : int(e^(log(1+(1)/(x^(2)))))/(x^(2)+(1)/(x^(2)))dx=(1)/(sqrt(2))tan^(-1).(x^(2)-1)/(sqrt(2)x)+c and STATEMENT-2 : e^(logx)= x if x gt 0 .

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: int("cosec x")/(log tan(x/2)) dx

(i) int(1)/((1+x^(2))tan ^(-1) x )dx " "(ii) int(e^(tan^(-1)x))/(1+x^(2))dx