\(\int\limits^{\frac{3}{2}}_0\frac{dx}{\sqrt{\left(4-x^2\right)^9}}\)
Tính tích phân :
\(I=\int\limits^1_0\frac{dx}{\left(x+1\right)^3}\)
1) \(\int\left(\frac{lnx}{2+lnx}\right)^2\)
2) \(\int\frac{dx}{\left(x+3\right)^3\left(x+5\right)^5}\)
3) \(\int\frac{xdx}{\sqrt{1+\sqrt[3]{x^2}}}\)
4) \(\int\frac{dx}{x^3.\sqrt[3]{2-x^3}}\)
5)\(\int\sqrt[3]{\frac{2-x}{2+x}}.\frac{1}{\left(2-x\right)^2}dx\)
Cho \(\int\limits^2_1\frac{ln\left(1+2x\right)}{x^2}dx=\frac{a}{2}.ln5+b.ln3+c.ln2\) , với a,b,c là các số nguyên. tính giá trị của a + 2(b+c).
1)\(\int\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}dx\)
2)\(\int\frac{dx}{\left(e^x+1\right)\left(x^2+1\right)}\)
3)\(\int\frac{1+2x\sqrt{1-x^2}+2x^2}{1+x+\sqrt{1+x^2}}\)dx
4)\(\int\frac{sin^6x+c\text{os}^6x}{1+6^x}dx\)
5)\(\int_0^{\frac{\pi}{2}}\frac{\sqrt{c\text{os}x}}{\sqrt{s\text{inx}}+\sqrt{c\text{os}x}}dx\)
6)\(\int\frac{x^4}{2^x+1}dx\)
7)\(\int_0^{\frac{\pi^2}{4}}sin\sqrt{x}dx\)
8)\(\int\sqrt[6]{1-c\text{os}^3x}.s\text{inx}.c\text{os}^5xdx\)
9)\(\int\sqrt{\frac{1}{4x}+\frac{\sqrt{x}+e^x}{\sqrt{x}.e^x}}dx\)
10)\(\int\frac{c\text{os}x+s\text{inx}}{\left(e^xs\text{inx}+1\right)s\text{inx}}dx\)
\(\int\frac{x}{\left(1+2x\right)^3}dx\)
\(\int\frac{1-x^2}{x+x^3}dx\)
\(\int\frac{tan^3x}{c\text{os}2x}dx\)
2) \(\int\frac{xe^x\left(4+4\left(s\text{inx}+c\text{os}x\right)+sin2x\right)}{\left(1+c\text{os}x\right)^2}\)
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
Tìm nguyên hàm các hàm số hữu tỉ sau :
a) \(\int\frac{x^2+2x-1}{\left(x-1\right)\left(x^2+1\right)}dx\)
b) \(\int\frac{x^2+1}{\left(x-1\right)^3\left(x+3\right)}dx\)
