原式=-5∫arctanxdx²
=-5x²arctanx+5∫x²darctanx
=-5x²arctanx+5∫x²/(1+x²) dx
=-5x²arctanx+5∫[1-1/(1+x²)]dx
=-5x²arctanx+5x-5arctanx+C
求-10x*arctan(x)的不定积分
原式=-5∫arctanxdx²
=-5x²arctanx+5∫x²darctanx
=-5x²arctanx+5∫x²/(1+x²) dx
=-5x²arctanx+5∫[1-1/(1+x²)]dx
=-5x²arctanx+5x-5arctanx+C