`\int`(x+1+$\frac{1}{x}$ )dx=...... `\int`(x²+3+$\frac{1}{x²}$ )dx=...... `\int`(x- $\frac{1}{2}$ )dx=..... `\int`(x²+ √3 )dx=....... `\int`( $\frac{x}{2}$ -$\frac{2}{x}$ )dx=.......... `\int`( $\frac{x^{2}}{3}$ +$\frac{3}{x^{2}}$ )dx=.......... `\int`( $\sqrt[]{x}$ -$\frac{1}{\sqrt[]{x}}$ )dx=.................. `\int`( $\frac{\sqrt[]{x}}{2}$ -$\frac{2}{\sqrt[]{x}}$ )dx=.........

Đáp án+Giải thích các bước giải:

$\displaystyle\int\left(x+1+\dfrac{1}{x}\right) \, dx=\dfrac{x^2}{2}+x+\ln |x| +C\\ \displaystyle\int\left(x^2+3+\dfrac{1}{x^2}\right) \, dx=\dfrac{x^3}{3}+3x-\dfrac{1}{x} +C\\ \displaystyle\int\left(x-\dfrac{1}{2}\right) \, dx=\dfrac{x^2}{2}-\dfrac{1}{2}x +C\\ \displaystyle\int\left(x^2+\sqrt{3}\right) \, dx=\dfrac{x^3}{3}+\sqrt{3}x +C\\ \displaystyle\int\left(\dfrac{x}{2}-\dfrac{2}{x}\right) \, dx=\dfrac{x^2}{4}-2\ln |x|+C\\ \displaystyle\int\left(\dfrac{x^2}{3}+\dfrac{3}{x^2}\right) \, dx=\dfrac{x^3}{9}-\dfrac{3}{x}+C\\ \displaystyle\int\left(\sqrt{x}-\dfrac{1}{\sqrt{x}}\right) \, dx\\ =\displaystyle\int\left(x^\tfrac{1}{2}-x^{-\tfrac{1}{2}}\right) \, dx\\ =\dfrac{2}{3}x^\tfrac{3}{2}-2x^\tfrac{1}{2}+C\\ =\dfrac{2}{3}x\sqrt{x}-2\sqrt{x}+C\\ \displaystyle\int\left(\dfrac{\sqrt{x}}{2}-\dfrac{2}{\sqrt{x}}\right) \, dx\\ =\displaystyle\int\left(\dfrac{1}{2}x^\tfrac{1}{2}-2x^{-\tfrac{1}{2}}\right) \, dx\\ =\dfrac{1}{2}.\dfrac{2}{3}x^\tfrac{3}{2}-2.2x^\tfrac{1}{2}+C\\ =\dfrac{1}{3}x\sqrt{x}-4\sqrt{x}+C.$