Integration of ax3+ bx / x4+ c2dx Share with your friends Share 5 Tanveer Sofi answered this we can write∫ax3+bxx4+c2dx=∫ax3x4+c2dx+∫bxx4+c2dxConsider the integral ∫ax3x4+c2dx firstLet x4+c2=u⇒4x3 dx= du Therefore, ∫ax3x4+c2dx =a4∫1udu=a4lnu+C1=a4lnx4+c2+C1 As, ∫1xdx=lnxNow consider the integral ∫bxx4+c2dx let x2=v⇒2x dx= dvTherefore, ∫bxx4+c2dx=b2∫1v2+c2dv=b2ctan-1vc+C2 As, ∫ax2+a2dx=tan-1xa=b2ctan-1x2c+C1Hence, we can write∫ax3+bxx4+c2dx=∫ax3x4+c2dx+∫bxx4+c2dx =a4lnx4+c2+C1 + b2ctan-1x2c+C1=a4lnx4+c2 +b2ctan-1x2c+C (Where, C1+C2=C) 13 View Full Answer
