Question

Integral of arctan(8x) dx.

Answer 1

The integration of arctan(8x) involves integration by parts and understanding of trigonometric functions. It results in x times arctan(8x) minus a secondary integral involving the derivative of arctan(8x).

Step-by-step explanation:

The integral of arctan(8x) with respect to x can be found using integration techniques such as integration by parts. The integral of arctan(8x) is given by x arctan(8x) minus the integral of x times the derivative of arctan(8x), which involves the use of the chain rule to differentiate arctan(8x). This process requires some familiarity with trigonometric integrals, specifically how the sin of arctan may be used in related problems. Ultimately, an integral solver or manual calculation results in the antiderivative of arctan(8x).

Answer 2

we are asked to determine the integral tan^(-1)(8 x) dx. we use the inverse property of trigonometric equation in integral calculus such that the answer is integral tan^(-1)(8 x) dx. = x tan^(-1)(8 x)-1/16 log(64 x^2+1)+ C where C is a constant.