∫dx/sinxcos4x
∫dx/sinxcos4x=∫[(sin2x+cos2x)/(sinxcos4x)]dx=∫(sinx/cos4)dx+∫(1/sinxcos2x)dx=-∫(1/cos4x)dcos+∫[(sin2x+cos2x)/(sinxcos2x)]dx=(1/3)sec3x+∫(sinx/cos2)dx+∫(dx/sinx)=(1/3)sec3x+secx+ln∣cscx-cotx∣+C
∫dx/sinxcos4x
∫dx/sinxcos4x=∫[(sin2x+cos2x)/(sinxcos4x)]dx=∫(sinx/cos4)dx+∫(1/sinxcos2x)dx=-∫(1/cos4x)dcos+∫[(sin2x+cos2x)/(sinxcos2x)]dx=(1/3)sec3x+∫(sinx/cos2)dx+∫(dx/sinx)=(1/3)sec3x+secx+ln∣cscx-cotx∣+C
