Bài tập 3.15 trang 166 SBT Toán 12
Bài tập 3.15 trang 166 SBT Toán 12
\(\mathop \smallint \nolimits x{\rm{}}\sqrt {x - 1} dx\) bằng :
A. \({(x - 1)^{\frac{5}{2}}} + {(x - 1)^{\frac{3}{2}}} + C\)
B. \(\frac{2}{{15}}\left[ {3{{(x - 1)}^{\frac{5}{2}}} - 5{{(x - 1)}^{\frac{3}{2}}}} \right] + C\)
C. \(\frac{2}{{15}}\left[ {3{{(x - 1)}^{\frac{5}{2}}} + 5{{(x - 1)}^{\frac{3}{2}}}} \right] + C\)
D. \(\frac{1}{{15}}\left[ {3{{(x - 1)}^{\frac{5}{2}}} + 5{{(x - 1)}^{\frac{3}{2}}}} \right] + C\)
\(\begin{array}{l}
\int {x\sqrt {x - 1} dx = \int {\left( {x - 1} \right)\sqrt {x - 1} dx + \int {\sqrt {x - 1} dx} } } \\
= \frac{2}{5}{\left( {x - 1} \right)^{\frac{5}{2}}} + \frac{2}{3}{\left( {x - 1} \right)^{\frac{3}{2}}} + C\\
= \frac{2}{{15}}\left[ {3{{\left( {x - 1} \right)}^{\frac{5}{2}}} + 5{{\left( {x - 1} \right)}^{\frac{3}{2}}}} \right] + C
\end{array}\)
Chọn đáp án C
-- Mod Toán 12
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