A) \[10\]
B) \[21\]
C) \[36\]
D) \[42\]
Correct Answer: D
Solution :
[d] Put \[t={{y}^{2}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,I=\int{\frac{2ydy}{{{(1+y)}^{8}}}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\int{\frac{(2y+2)-2}{{{(1+y)}^{8}}}}dy\] \[=2\left[ \int{\frac{1}{{{(1+y)}^{8}}}-\frac{1}{{{(1+y)}^{7}}}dy} \right]\] \[=\frac{2}{7{{(1+y)}^{7}}}-\frac{1}{3{{(1+y)}^{6}}}\] \[=\frac{2}{7{{\left( 1+\sqrt{t} \right)}^{7}}}-\frac{1}{3{{\left( 1+\sqrt{t} \right)}^{6}}}\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{p}_{1}}=6,\,\,{{p}_{2}}=7\]
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