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$If \int \frac{(\sqrt{x})^{5}}{(\sqrt{x})^{7} + x^{6}} d x = a \ln \frac{x^{k}}{x^{k} + 1} + c, the value of a and k, respectively, are$

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52 and 25

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Correct option is B

∫dx(x)2+(x)7=∫dx(x)71+1(x)5 Put 1(x)5=y,dydx=−52(x)7∴I=∫−2dy5(1+y)=−25ln⁡|1+y|+c=25ln⁡11+1(x)5∴a=25,k=52

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If ∫(x)5(x)7+x6dx=aln⁡xkxk+1+c, the value of a and k, respectively, are

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$If \int \frac{(\sqrt{x})^{5}}{(\sqrt{x})^{7} + x^{6}} d x = a \ln \frac{x^{k}}{x^{k} + 1} + c, the value of a and k, respectively, are$