A) 4
B) 5
C) 6
D) none
Correct Answer: B
Solution :
\[I=\int{\frac{2x+3}{({{x}^{2}}+3x)({{x}^{2}}+3x+2)+1}}dx\] Put \[{{x}^{2}}+3x=t\] \[\Rightarrow \] \[(2x+3)dx=dt\] \[\Rightarrow \] \[I=\int{\frac{dt}{t(t+2)+1}}\] \[=\int{\frac{dt}{{{(t+1)}^{2}}}}\] \[=C-\frac{1}{t+1}\] \[=C-\frac{1}{{{x}^{2}}+3x+1}\] \[\therefore \] \[f(1)=5\]You need to login to perform this action.
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