1, \(\int\dfrac{dx}{1+\sqrt{x}}\)

2, \(\int\dfrac{sinx.cos^3x}{1+sin^2x}dx\)

1, \(\int\dfrac{x^3dx}{\left(x^8-4\right)^2}\)

2, \(\int\dfrac{2x+1}{x^4+2x^2+3x^2+2x-3}dx\)

3, \(\int\dfrac{sin\sqrt[3]{x}}{\sqrt[3]{x^2}}dx\)

4, \(\int\dfrac{dx}{sin^2x+2cos^2x}\)

5, \(\int\dfrac{sinx+cosx}{3+sin2x}dx\)

mọi người tính giúp em mấy cái nguyên hàm với :

1, \(\int\dfrac{x^2-1}{x^4+1}dx\)

2, \(\int\dfrac{dx}{3x^2-3}\)

3, \(\int\dfrac{dx}{1+sinx}\)

4, \(\int\dfrac{sinxdx}{\sqrt{cos2x}}\)

5, \(\int\dfrac{xdx}{\sqrt[3]{1-3x}}\)

6, \(\int2^{2x}.3^{3x}.4^xdx\)

7,\(\int\dfrac{dx}{xlnx.ln\left(lnx\right)}\)

8, \(\int\dfrac{dx}{sinx.cos^3x}\)

9, \(\int\dfrac{cos2xdx}{sin^2x.cos^2x}\)

10, \(\int\dfrac{dx}{\sqrt{2x}-\sqrt{2x+1}}\)

giải bpt logarit đưa về cùng cơ số

1, \(2lg\left[\left(x-1\right)\sqrt{5}\right]>lg\left(x-5\right)+1\)

2, \(log_{\dfrac{1}{2}}\left[log_2\left(3^x+1\right)\right]>-1\)

3, \(log_x\dfrac{3x-1}{x^2+1}>0\)

4, \(\left(0,08\right)^{log_{0,5-x}x}\ge\left(\dfrac{5\sqrt[]{2}}{2}\right)^{log_{x-0,5}\left(2x-1\right)}\)

- Ai đó làm giúp với nhé

bpt logarit đặt ẩn phụ

1, \(log_3x.log_2x< log_3x^2+log_2\dfrac{x}{4}\)

2, \(log_2\left(2^x-1\right).log_{\dfrac{1}{2}}\left(2^{x+1}-2\right)>-2\)

3, \(x^{lg_x^2-3lgx+1}>1000\)

4, \(6^{log_6^2x}+x^{log_6x}\le12\)

bpt logarit đưa về cùng cơ số :

1, \(2lg\left[\left(x-1\right)\sqrt{5}\right]>lg\left(x-5\right)+1\)

2, \(log_{\dfrac{1}{2}}\left[log_2\left(3^x+1\right)\right]>-1\)

3, \(log_x\dfrac{3x-1}{x^2+1}>0\)

4, \(\left(0,08\right)^{log_{x-0,5}x}\ge\left(\dfrac{5\sqrt{2}}{2}\right)^{log_{x-0,5}\left(2x-1\right)}\)

\(x^{log_29}=x^2.3^{log_2x}-x^{log_23}\)

giải hộ pt trên với

1, \(log_{5x}\dfrac{5}{x}+log^{2_{ }}_5x=1\)

2, \(log_5\left(5^x-1\right).log_{25}\left(5^{x+1}-5\right)=1\)

3, \(2\left(log_3x^{ }\right)^2=log_3x.log_3\left(\sqrt{2x+1}-1\right)\)

- giải hộ 3 phương trình trên với