∫csc(ax)dx=a1∫a⋅csc(ax)dxu=ax⇒du=adxSubstituteu.a1∫a⋅csc(ax)dx=a1∫cscudu∫cscudu=∫cscucscu+cotucscu+cotudu==−∫−cscu+cotucsc2u+cscu⋅cotuduv=cscu+cotuLet′stakederivativeofv.dv=−(cscu⋅cotu+csc2u)duSubstitutev.−∫−cscu+cotu(csc2u+cscu⋅cotu)du=−∫vdv==−ln∣v∣+C==−ln∣cscu+cotu∣+C==−ln∣csc(ax)+cot(ax)∣+C∫csc(ax)dx=−a1ln∣csc(ax)+cot(ax)∣+C
Comments
Leave a comment