Integrate: 1 / (1+ square root x) ^8

Answers (1)

Solution:    

                 I=int frac1(1+sqrtx)^8dx hspace0.5cmput hspace0.5cm1+sqrtx=t \ \ Rightarrow hspace0.5cmfrac12sqrtxdx=dt \ Rightarrow hspace0.5cmI=int frac2sqrtxt^8dt \ Rightarrow hspace0.5cmI=2int fract-1t^8dt \ Rightarrow hspace0.5cmI=2int (frac1t^7-frac1t^8)dt

                \ Rightarrow hspace0.5cmI=2[-frac16t^6-frac17t^7]+c \ Rightarrow hspace0.5cmI=2[-frac16x^3-frac17x^frac72]+c

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