Lời giải:
\(\int\frac{x^2+3x+3}{x^3-3x+2}dx=\int\frac{(x+2)(x-1)+2(x+2)+1}{(x-1)^2(x+2)}dx=\int\frac{7dx}{3(x-1)^2}+\int\frac{8dx}{9(x-1)}+\int\frac{dx}{9(x+2)}\)\(=\frac{-7}{3(x-1)}+\frac{8}{9}\ln|x-1|+\frac{1}{9}\ln|x+2|+c\)
1) \(\int\frac{xdx}{1+\sqrt{x-1}}\)
2) \(\int\frac{sin2xdx}{\cos^3x-\sin^2x-1}\)
3) \(\int\frac{dx}{1+\sqrt{x}+\sqrt{1+x}}\)
4) \(\int\frac{dx}{3x^3+x^2-4x}\)
5) \(\int\frac{dx}{\sqrt{9-x^2}}\)
Tìm nguyên hàm các hàm số hữu tỉ sau :
a) \(\int\frac{3x+2}{x^2+3x-3}dx\)
b)\(\int\frac{2x-3}{x^2+4x+4}dx\)
Tìm các nguyên hàm sau:
a) \(\int (3x^2-2x-4)dx \)
b) \(\int(\sin3x-\cos4x)dx \)
c) \(\int(e^{-3x}-4^x)dx \)
d) \(\int\ln(x)dx \)
e) \(\int(x.e^x)dx \)
f) \(\int(x+1).\sin(x)dx \)
g) \(\int x.\ln(x)dx \)
\(\int\dfrac{3x^2+3x+3}{x+2x}dx\)
Tìm các nguyên hàm sau
1.\(\int\frac{9x^2}{\sqrt{1-x^3}}dx\)
2.\(\int\frac{1}{\sqrt{x}\left(1+\sqrt{x}\right)^3}dx\)
3.\(\int\frac{x}{\sqrt{2x+3}}dx\)
4.\(\int\) \(\frac{e^{2x}}{\sqrt{1+e^x}}\) dx
5.\(\int\frac{\sqrt[3]{1+lnx}}{x}dx\)
6.\(\int\) cosxsin3xdx
7.\(\int\) (x2+2x-1)exdx
8.\(\int\) excosxdx
9.\(\int\) xsin(2x+1)dx
10.\(\int\) (1-2x)e3xdx
Tính:
\(\int\frac{3x-2}{x-3}dx\)
Tìm nguyên hàm sau:
$\displaystyle\int
\left(3x^2 - \frac{4}{x} + \sin3x - \cos4x + e^{2x+1} + 3^{2x-2} + 3\sqrt{x^4} + \frac{1}{\cos^2x} - \frac{1}{\sin^2x}\right) dx$
Tìm nguyên hàm các hàm số hữu tỉ sau :
a.) \(\int\frac{1}{x^2-3x+2}dx\)
b) \(\int\frac{1}{4x^2-3x-1}dx\)
Tìm nguyên làm các hàm số hữu tỉ sau :
a)
\(\int\frac{3x^2+3x+12}{\left(x-1\right)\left(x+2\right)}dx\)
b) \(\int\frac{x^2+2x+6}{\left(x-1\right)\left(x-2\right)\left(x-4\right)}dx\)
