If `alpha=int_0^1(e^9x+3tan^(-1)x)((12+9x^2)/(1+x^2))dx` where `tan^(-1)x` takes only principal values, then the value of `(log_e|1+alpha|-(3pi)/4)` is

int e^(tan^(-1)x)((1)/(1+x^(2)))dx=

int(e^(ln tan^(-1)x))/(1+x^(2))dx

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

The value of int e^(tan-1)x((1+x+x^(2))/(1+x^(2)))dx

Prove that int e^x (tan^-1 x+1/(1+x^2)) dx=e^x tan^-1x+c

If cos^(-1).(6x)/(1 + 9x^(2)) = -(pi)/(2) + 2 tan^(-1) 3x , then find the values of x

If cos^(-1)(6x)/(1+9x^(2))=-(pi)/(2)+tan^(-1)3x, then find the value of x.

The value of int_(1)^(e)((tan^(-1)x)/(x)+(log x)/(1+x^(2)))dx is tan e(b)tan^(-1)e tan^(-1)((1)/(e))(d) none of these

For real numbers alpha, beta, gamma and delta , if int((x^(2)-1)+tan^(-1)((x^(2)+1)/(x)))/((x^(4)+3x^(2)+1)tan^(-1)((x^(2)+1)/(x)))dx = alpha log_(e)(tan^(-1)((x^(2)+1)/(x)))+beta "tan"^(-1)((gamma(x^(2)-1))/(x))+delta tan ((x^(2)+1)/(x))+C where is an arbitrary constant, then the value of 10(alpha+betagamma+delta) is equal to........

Evaluate int_(log1//3)^(log3)tan((e^(x)-1)/(e^(x)+1))dx