Evaluate the integral. (Use C for the constant of integration.)
integral of arctan6tdt
To evaluate the integral, we use the formula for the integral of arctan(u):
∫ arctan(u) du = u * arctan(u) - ∫ (1 + u^2) / (1 + u^2) du
= u * arctan(u) - ∫ 1 du
= u * arctan(u) - u + C
In this case, u = 6t. So the integral of arctan(6t) dt is:
∫ arctan(6t) dt = (6t) * arctan(6t) - (6t) + C
= 6t * arctan(6t) - 6t + C
So the integral of arctan(6t) dt is given by 6t * arctan(6t) - 6t + C.