`\int`[2x(x-8)]dx=....... `\int`(2x+5)(x+1)dx=......... `\int`[x(x-3)²]dx=........... `\int`[x(x-1)³]dx=..... `\int` (x-2)(x+2)dx=........ Bài 3) `\int` $\frac{3x-4}{2}$ dx=...... `\int`$\frac{x+1}{\sqrt[]{x}}$ dx=.... `\int`$\frac{(x+2)²}{x}$ dx=........ `\int`$\frac{(x+2)³}{x}$ dx=.....

Đáp án+Giải thích các bước giải:

$\displaystyle \int  [2x(x-8)] \, dx=\displaystyle \int  (2x^2-16x) \, dx=\dfrac{2x^3}{3}-8x^2+C\\ \displaystyle \int (2x+5)(x+1) \, dx=\displaystyle \int (2 x^2 + 7 x + 5) \, dx=\dfrac{2x^3}{3}+\dfrac{7x^2}{2}+5x+C\\ \displaystyle \int x(x-3)^2 \, dx=\displaystyle \int (x^3-6x^2+9x) \, dx=\dfrac{x^4}{4}-2x^3+\dfrac{9x^2}{2}+C\\ \displaystyle \int x(x-1)^3 \, dx=\displaystyle \int (x^4-3x^3+3x^2-x) \, dx=\dfrac{x^5}{5}-\dfrac{3x^4}{4}+x^3-\dfrac{x^2}{2}+C\\ \displaystyle \int (x-2)(x+2) \, dx=\displaystyle \int (x^2-4) \, dx=\dfrac{x^3}{3}-4x+C\\ 3)\\ \displaystyle \int \dfrac{3x-4}{2} \, dx=\dfrac{1}{2}\displaystyle \int (3x-4) \, dx=\dfrac{3x^2}{4}-2x+C\\ \displaystyle \int \dfrac{x+1}{\sqrt{x}} \, dx\\ =\displaystyle \int \left(\sqrt{x}+\dfrac{1}{\sqrt{x}}\right) \, dx\\ =\displaystyle\int\left(x^\tfrac{1}{2}+x^{-\tfrac{1}{2}}\right) \, dx\\ =\dfrac{2}{3}x^\tfrac{3}{2}+2x^\tfrac{1}{2}+C\\ =\dfrac{2}{3}x\sqrt{x}+2\sqrt{x}+C\\ \displaystyle \int \dfrac{(x+2)^2}{x} \, dx\\ =\displaystyle \int \dfrac{x^2+4x+4}{x} \, dx\\ =\displaystyle \int \left(x+4+\dfrac{4}{x}\right) \, dx\\ =\dfrac{x^2}{2}+4x+4\ln|x|+C\\ \displaystyle \int \dfrac{(x+2)^3}{x} \, dx\\ =\displaystyle \int \dfrac{x^3 + 6 x^2 + 12 x + 8}{x} \, dx\\ =\displaystyle \int \left(x^2 + 6 x + 12  + \dfrac{8}{x}\right) \, dx\\ =\dfrac{x^3}{3}+3x^2+12x+8\ln|x|+C.$