Integrate : ( x^2 +1 ) square root (x+1)

Answers (1)

Solution: We have ,

            \ I=int (x^2+1)sqrtx+1hspace0.1cmdx

        Put ,   x+1=tRightarrow dx=dt

         Rightarrow  (x^2+1)=(t^2-2t+2)

       	herefore      I=int (t^frac52-2t^frac32+2t^frac12)dt

     Rightarrow     I=frac27 t^frac72-frac45t^frac52+frac43t^frac32+c

    Rightarrow    I=2[frac17(x+1)^frac72-frac25(x+1)^frac52+frac23(x+1)^frac32]+c.

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