Question

BRAINLIEST! CALCULUS HELPPlease show steps and work so I can understand.

Answer 1

Separating the integral, we get the integral of 1/x minus the integral of 4/(x^2+1). From memory, I know that the integral of 1/x is ln(x). Next, I can separate the 4 from 4/(x^2+1), and I know from memory that the integral of 1/(x^2+1) is arctan(x). Therefore, your answer is ln(x)+C-4arctan(x)+C=ln(x)+4arctanx+C (Since C simply represents any number, we don't need to make it 2C. In addition, the C after 4arctan(x) and ln(x) could be different, so C-C would be some constant C too in this case)

Answer 2

∫[(1/x) - 4/x²+1)]dx = ∫(1/x)dx - 4∫(1/x²+1).dx

∫(1/x)dx  = lnx + c  and - 4∫(1/x²+1).dx = -4 arctanx +c



∫(1/x)dx - 4∫(1/x²+1).dx = lnx -4 arctanx +c (note that arctanx = tan⁻¹x)