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Question

Evaluate the following integrals:

x2x4+x2-2dx

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Solution

Let I=x2x4+x2-2dxWe expressx2x4+x2-2=x2x4+2x2-x2-2 =x2x2+2x2-1 =Ax2+2+Bx2-1x2=Ax2-1+Bx2+2Equating the coefficients of x2 and constants, we get1=A+B and 0=-A+2Bor A=23 and B=13I=23x2+2+13x2-1dx =231x2+2dx+131x2-1 dx =23tan-1x2+16logx-1x+1+cHence, x2x4+x2-2dx=23tan-1x2+16logx-1x+1+c

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