Tìm ∫(√x/2+2/√x)dx

Question

Tìm \(\int \left(\frac{\sqrt{x} }{2} +\frac{2}{\sqrt{x} } \right) {\rm d}x\)
 

A. \(\frac{2}{3} \sqrt{x^{3} } +4\sqrt{x} +C. \)

B. \(\frac{1}{3} \sqrt{x^{3} } +4\sqrt{x} +C.\)

C. \(\frac{2}{3} \sqrt{x^{3} } -\sqrt{x} +C. \)

D. \(\frac{1}{3} \sqrt{x^{3} } -4\sqrt{x} +C.\)
 

Answer 1

Chọn B

Ta có:

 \(\int \left(\frac{\sqrt{x} }{2} +\frac{2}{\sqrt{x} } \right) {\rm d}x=\frac{1}{2} \int x^{\frac{1}{2} }  {\rm d}x+4\int \frac{1}{2\sqrt{x} }  {\rm d}x\)

\(=\frac{1}{3} x^{\frac{3}{2} } +4\sqrt{x} +C =\frac{1}{3} \sqrt{x^{3} } +4\sqrt{x} +C.\)