If `alpha=int_0^1(e^9x+3tan^((-1)x))((12+9x^2)/(1+x^2))dxw h e r etan^(-1)` takes only principal values, then the value of `((log)_e|1+alpha|-(3pi)/4)i s`

If alpha=int_(0)^(1)(e^(9x+3tan^(-1)x))((12+9x^(2))/(1+x^(2)))dx wheretan ^(-1) takes only principal values,then the value of (log_(e)|1+alpha|-(3 pi)/(4))is

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

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

If alpha=int_(2)^(3) (2xdx)/(x^2+1) , then find the value of e^alpha

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

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

The value of int_(1//e )^(e )(|log x|)/(x^(2))dx , is

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

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

int (27 e ^(9x) + e ^( 12 x )) ^(1//3) dx is equal to