A) \[\frac{1}{6}(8x+11)\sqrt{4x+7}+C\]
B) \[\frac{1}{6}(8x+13)\sqrt{4x+7}+C\]
C) \[\frac{1}{6}(8x+9)\sqrt{4x+7}+C\]
D) \[\frac{1}{6}(8x+15)\sqrt{4x+7}+C\]
Correct Answer: A
Solution :
\[I=\int{\frac{8x+13}{\sqrt{4x+7}}}dx=\int{\frac{2(4x+7)-1}{\sqrt{4x+7}}.dx}\] \[=2\int{\sqrt{4x+7}}dx-\int{\frac{dx}{\sqrt{4x+7}}=2.\frac{{{(4x+7)}^{3/2}}}{4.\frac{3}{2}}}\] \[-\frac{{{(4x+7)}^{1/2}}}{4.\frac{1}{2}}+C\] \[=\frac{1}{3}(4x+7)\sqrt{4x+7}-\frac{1}{2}\sqrt{4x+7}+C\] \[=\frac{\sqrt{4x+7}}{6}.(8x+11)+C\]
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