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  • If the Integral of x^26 .(x-1)^17 .(5x-3) =x^27.(x-1)^18 / k + c

If the Integral of x^26 .(x-1)^17 .(5x-3) =x^27.(x-1)^18 / k + c

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Solution:   We have ,

                   I=int x^26cdot (x-1)^17cdot (5x-3)dx=fracx^27cdot (x-1)^18k+c

                Differentiating both sides gives

              Rightarrow       x^26cdot (x-1)^17cdot(5x-3)=frac1k[x^27cdot18(x-1)^17+(x-1)^1827x^26]=fracx^26(x-1)^17k[18x+27(x-1)]

             Rightarrow                                                                             =9fracx^26(x-1)^17k(5x-3)

                                 k=9.             

Posted by

Deependra Verma

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