\(I=\int\limits^1_0\frac{x+1-1dx}{\left(x+1\right)^3}=\int\limits^1_0\frac{dx}{\left(x+1\right)^2}-\int\limits^1_0\frac{dx}{\left(x+1\right)^3}=x+1|^1_0+\frac{1}{2\left(x+1\right)^2}|^1_0=\frac{1}{8}\)
I=\(\int\limits^{\frac{\pi}{6}}_0\)\(\frac{tan^4xdx}{cos2x}\)
J=\(\int\limits^3_1\)\(\frac{3+lnx}{\left(x+1\right)^2}\)
K=\(\int\limits^1_0\)\(\frac{\left(2+xe^x\right)}{x^2+2x+1}\)dx
\(\int\limits^{\frac{3}{2}}_0\frac{dx}{\sqrt{\left(4-x^2\right)^9}}\)
Tính tích phân bất định hàm số hữu tỉ sau :
a) \(\int\frac{dx}{\sqrt{\left(1-x^2\right)^3}}\)
b) \(\int\frac{dx}{\sqrt{x^2+2x+3}}\)
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)\(\int\sqrt[3]{\frac{2-x}{2+x}}.\frac{1}{\left(2-x\right)^2}dx\)
\(\int\frac{x}{\left(1+2x\right)^3}dx\)
\(\int\frac{1-x^2}{x+x^3}dx\)
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) \(\int\frac{x^2+1}{\left(x-1\right)^3\left(x+3\right)}dx\)
Cho \(\int\left(x\right)dx=x\sqrt{x^2+1}\). Tìm I=\(\int x.f\left(x^2\right)dx\)
Tính \(I=\int x.\ln\left(x+1\right)dx\)
Tính các nguyên hàm sau :
a) \(\int x\left(3-x\right)^5dx\)
b) \(\int\left(2^x-3^x\right)^2dx\)
c) \(\int x\sqrt{2-5x}dx\)
d) \(\int\dfrac{\ln\left(\cos x\right)}{\cos^2x}dx\)
e) \(\int\dfrac{x}{\sin^2x}dx\)
\(\int\dfrac{x+1}{\left(x-2\right)\left(x+3\right)}dx\)
h) \(\int\dfrac{1}{1-\sqrt{x}}dx\)
i) \(\int\sin3x\cos2xdx\)
k) \(\int\dfrac{\sin^3x}{\cos^2x}dx\)
l) \(\int\dfrac{\sin x\cos x}{\sqrt{a^2\sin^2x+b^2\cos^2x}}dx\) (\(a^2\ne b^2\))