∫(根号下arctanx/1+x^2)dx ；∫((arcsinx)^2/根号下1-x^2)dx；∫e^xcos(e^x+1)dx

∫(根号下arctanx/1+x^2)dx ；∫((arcsinx)^2/根号下1-x^2)dx；∫e^xcos(e^x+1)dx

∫√arctanxdx/(1+x^2)
=∫√arctanxdarctanx
=(2/3)√(arctanx)^3+C
∫(arcsinx)^2dx/√(1-x^2)
=∫(arcsinx)^2darcsinx
=(1/3)(arcsinx)^3+C
∫e^xcos(e^x+1)dx
=∫cos(e^x+1)d(e^x+1)
=sin(e^x+1)+C