Let `inte^(3x)tan^(- 1)e^x dx=e^(3x)f(x)+1/6g(x)+C` such that `f(0)=pi/12,g(0)=I n(2/e) and C` is constant of integration, then

int_( Let )^( Let )e^(3x)tan^(-1)e^(x)dx=e^(3x)f(x)+(1)/(6)g(x)+C such that f(0)=(pi)/(12),g(0)=In((2)/(e)) and C is constant of integration,then

Let int(dx)/(sqrt(x^(2)+1)-x)=f(x)+C such that f(0)=0 and C is the constant of integration, then the value of f(1) is

Let int(dx)/(sqrt(x^(2)+1)-x)=f(x)+C such that f(0)=0 and C is the constant of integration, then the value of f(1) is

If I=int(tan^(-1)(e^(x)))/(e^(x)+e^(-x))dx=([tan^(-1)(f(x))]^(2))/(2)+C (where C is the constant of integration), then the range of y=f(x) AA x in R is

If I=int(tan^(-1)(e^(x)))/(e^(x)+e^(-x))dx=([tan^(-1)(f(x))]^(2))/(2)+C (where C is the constant of integration), then the range of y=f(x) AA x in R is

If the integral int(lnx)/(x^(3))dx=(f(x))/(4x^(2))+C , where f(e )=-3 and C is the constant of integration, then the value of f(e^(2)) is equal to

If the integral int(lnx)/(x^(3))dx=(f(x))/(4x^(2))+C , where f(e )=-3 and C is the constant of integration, then the value of f(e^(2)) is equal to

if int xe^(2x) dx = e^(2x).f(x)+c , where c is the constant of integration, then f(x) is

Let f(x) be a cubic polynomial with leading coefficient unity such that f(0)=1 and all the roots of f(x)=0 are also roots of f(x)=0. If f(x)dx=g(x)+C, where g(0)=(1)/(4) and C is constant of integration,then g(3)-g(1) is equal to

int((f'(x)g(x)+f(x)g'(x)))/((1+(f(x)g(x))^(2)))dx is where C is constant of integration