1) \(\int\limits^2_1\dfrac{\sqrt{x^2-1}}{x}dx\)
2) \(\int x.\sqrt{1-x^4}dx\)
3)\(\int\dfrac{1}{x^2.\sqrt{25-x^2}}dx\)
4) \(\int\dfrac{\sqrt{x^2-9}}{x^3}dx\)
Những câu hỏi liên quan
Tính nguyên hàm của:1, intdfrac{x^3}{x-2}dx2, intdfrac{dx}{xsqrt{x^2+1}}3, int(dfrac{5}{x}+sqrt{x^3})dx4, intdfrac{xsqrt{x}+sqrt{x}}{x^2}dx5, intdfrac{dx}{sqrt{1-x^2}}
Đọc tiếp
Tính nguyên hàm của:
1, \(\int\)\(\dfrac{x^3}{x-2}dx\)
2, \(\int\)\(\dfrac{dx}{x\sqrt{x^2+1}}\)
3, \(\int\)\((\dfrac{5}{x}+\sqrt{x^3})dx\)
4, \(\int\)\(\dfrac{x\sqrt{x}+\sqrt{x}}{x^2}dx\)
5, \(\int\)\(\dfrac{dx}{\sqrt{1-x^2}}\)
a. \(\int\dfrac{x^3}{x-2}dx=\int\left(x^2+2x+4+\dfrac{8}{x-2}\right)dx=\dfrac{1}{3}x^3+x^2+4x+8ln\left|x-2\right|+C\)
b. \(\int\dfrac{dx}{x\sqrt{x^2+1}}=\int\dfrac{xdx}{x^2\sqrt{x^2+1}}\)
Đặt \(\sqrt{x^2+1}=u\Rightarrow x^2=u^2-1\Rightarrow xdx=udu\)
\(I=\int\dfrac{udu}{\left(u^2-1\right)u}=\int\dfrac{du}{u^2-1}=\dfrac{1}{2}\int\left(\dfrac{1}{u-1}-\dfrac{1}{u+1}\right)du=\dfrac{1}{2}ln\left|\dfrac{u-1}{u+1}\right|+C\)
\(=\dfrac{1}{2}ln\left|\dfrac{\sqrt{x^2+1}-1}{\sqrt{x^2+1}+1}\right|+C\)
c. \(\int\left(\dfrac{5}{x}+\sqrt{x^3}\right)dx=\int\left(\dfrac{5}{x}+x^{\dfrac{3}{2}}\right)dx=5ln\left|x\right|+\dfrac{2}{5}\sqrt{x^5}+C\)
d. \(\int\dfrac{x\sqrt{x}+\sqrt{x}}{x^2}dx=\int\left(x^{-\dfrac{1}{2}}+x^{-\dfrac{3}{2}}\right)dx=2\sqrt{x}-\dfrac{1}{2\sqrt{x}}+C\)
e. \(\int\dfrac{dx}{\sqrt{1-x^2}}=arcsin\left(x\right)+C\)
Đúng 1
Bình luận (1)
Tính :
a) intlimits^2_{-1}left(5x^2-x+e^{0,5x}right)dx
b) intlimits^2_{0,5}left(2sqrt{x}+dfrac{3}{x^2}+cos xright)dx
c) intlimits^2_1dfrac{dx}{sqrt{2x+3}} (đặt tsqrt{2x+3} )
d) intlimits^2_1sqrt[3]{3x^3+4}x^2dx (đặt tsqrt[3]{3x^3+4} )
e) intlimits^2_{-2}left(x-2right)left|xright|dx
g) intlimits^0_1xcos xdx
h) intlimits^{dfrac{pi}{2}}_{dfrac{pi}{6}}dfrac{1+sin2x+cos2x}{sin x+cos x}dx
i) intlimits^{dfrac{pi}{2}}_0e^xsin xdx
k) intlimits^e_1x^2ln^2xdx
Đọc tiếp
Tính :
a) \(\int\limits^2_{-1}\left(5x^2-x+e^{0,5x}\right)dx\)
b) \(\int\limits^2_{0,5}\left(2\sqrt{x}+\dfrac{3}{x^2}+\cos x\right)dx\)
c) \(\int\limits^2_1\dfrac{dx}{\sqrt{2x+3}}\) (đặt \(t=\sqrt{2x+3}\) )
d) \(\int\limits^2_1\sqrt[3]{3x^3+4}x^2dx\) (đặt \(t=\sqrt[3]{3x^3+4}\) )
e) \(\int\limits^2_{-2}\left(x-2\right)\left|x\right|dx\)
g) \(\int\limits^0_1x\cos xdx\)
h) \(\int\limits^{\dfrac{\pi}{2}}_{\dfrac{\pi}{6}}\dfrac{1+\sin2x+\cos2x}{\sin x+\cos x}dx\)
i) \(\int\limits^{\dfrac{\pi}{2}}_0e^x\sin xdx\)
k) \(\int\limits^e_1x^2\ln^2xdx\)
1.\(\int\dfrac{\sin2x}{\cos^4x-4}dx\)
2.\(\int\sqrt{1-x^2}dx\)
3.\(\int\dfrac{xdx}{\sqrt{1+x^4}}dx\)
giúp mình với mn
Tính các tích phân sau :
a) intlimits^4_{-2}left(dfrac{x-2}{x+3}right)^2dx (đặt tx+3 )
b) intlimits^6_{-4}left|x+3right|-left|x-4right|dx
c) intlimits^2_{-3}dfrac{dx}{sqrt{x+7}+3} (đặt tsqrt{x+7} hoặc tsqrt{x+7}+3 )
d) intlimits^{dfrac{pi}{2}}_0dfrac{cos x}{1+4sin x}dx
e) intlimits^2_1dfrac{x^9}{x^{10}+4x^5+4}dx (đặt tx^5 )
g) intlimits^3_0left(x+2right)e^{2x}dx
h) intlimits^5_2dfrac{sqrt{4+x}}{x}dx (đặt tsqrt{4+x} )
Đọc tiếp
Tính các tích phân sau :
a) \(\int\limits^4_{-2}\left(\dfrac{x-2}{x+3}\right)^2dx\) (đặt \(t=x+3\) )
b) \(\int\limits^6_{-4}\left|x+3\right|-\left|x-4\right|dx\)
c) \(\int\limits^2_{-3}\dfrac{dx}{\sqrt{x+7}+3}\) (đặt \(t=\sqrt{x+7}\) hoặc \(t=\sqrt{x+7}+3\) )
d) \(\int\limits^{\dfrac{\pi}{2}}_0\dfrac{\cos x}{1+4\sin x}dx\)
e) \(\int\limits^2_1\dfrac{x^9}{x^{10}+4x^5+4}dx\) (đặt \(t=x^5\) )
g) \(\int\limits^3_0\left(x+2\right)e^{2x}dx\)
h) \(\int\limits^5_2\dfrac{\sqrt{4+x}}{x}dx\) (đặt \(t=\sqrt{4+x}\) )
1.\(\int_0^{\dfrac{\pi}{4}}\dfrac{\sin2x}{\sqrt{1+\cos^4x}}dx\)
2.\(\int_0^{ln3}\dfrac{e^x}{\sqrt{e^x+1}+1}dx\)
3.\(\int_1^2\dfrac{3x+1}{\sqrt{x^2+3x+9}}dx\)
4.\(\int\limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}}\sin x\sqrt{3+\cos^6x}dx\)
Tính các tích phân sau
1.Iintlimits^{frac{Pi}{4}}_0 (x+1)sin2xdx
2.Iintlimits^2_1frac{x^2+3x+1}{x^2+x}dx
3.Iintlimits^2_1frac{x^2-1}{x^2}lnxdx
4. Iintlimits^1_0xsqrt{2-x^2}dx
5.Iintlimits^1_0frac{left(x+1right)^2}{x^2+1}dx
6. Iintlimits^5_1frac{dx}{1+sqrt{2x-1}}
7. Iintlimits^3_1frac{1+lnleft(x+1right)}{x^2}dx
8.Iintlimits^1_0frac{x^3}{x^4+3x^2+2}dx
9. Iintlimits^{frac{Pi}{4}}_0xleft(1+sin2xright)dx
10. Iintlimits^3_0frac{x}{sqrt{x+1}}dx
Đọc tiếp
Tính các tích phân sau
1.I=\(\int\limits^{\frac{\Pi}{4}}_0\) (x+1)sin2xdx
2.I=\(\int\limits^2_1\frac{x^2+3x+1}{x^2+x}dx\)
3.I=\(\int\limits^2_1\frac{x^2-1}{x^2}lnxdx\)
4. I=\(\int\limits^1_0x\sqrt{2-x^2}dx\)
5.I=\(\int\limits^1_0\frac{\left(x+1\right)^2}{x^2+1}dx\)
6. I=\(\int\limits^5_1\frac{dx}{1+\sqrt{2x-1}}\)
7. I=\(\int\limits^3_1\frac{1+ln\left(x+1\right)}{x^2}dx\)
8.I=\(\int\limits^1_0\frac{x^3}{x^4+3x^2+2}dx\)
9. I=\(\int\limits^{\frac{\Pi}{4}}_0x\left(1+sin2x\right)dx\)
10. I=\(\int\limits^3_0\frac{x}{\sqrt{x+1}}dx\)
https://i.imgur.com/Pe6vPSJ.jpg
chứng minh:
\(\int\limits^1_0\dfrac{ln\left(x+\sqrt{1-x^2}\right)}{x}dx=\dfrac{3}{4}\int\limits\dfrac{ln\left(1+x\right)}{x}^1_0dx\)
Hãy chỉ ra kết quả nào dưới đây đúng :
a) intlimits^{dfrac{pi}{2}}_0sin xdx+intlimits^{dfrac{3pi}{2}}_{dfrac{pi}{2}}sin xdx+intlimits^{2pi}_{dfrac{3pi}{2}}sin xdx0
b) intlimits^{dfrac{pi}{2}}_0left(sqrt[3]{sin x}-sqrt[3]{cos x}right)dx0
c) intlimits^{dfrac{1}{2}}_{-dfrac{1}{2}}lndfrac{1-x}{1+x}dx0
d) intlimits^2_0left(dfrac{1}{1+x+x^2+x^3}+1right)dx0
Đọc tiếp
Hãy chỉ ra kết quả nào dưới đây đúng :
a) \(\int\limits^{\dfrac{\pi}{2}}_0\sin xdx+\int\limits^{\dfrac{3\pi}{2}}_{\dfrac{\pi}{2}}\sin xdx+\int\limits^{2\pi}_{\dfrac{3\pi}{2}}\sin xdx=0\)
b) \(\int\limits^{\dfrac{\pi}{2}}_0\left(\sqrt[3]{\sin x}-\sqrt[3]{\cos x}\right)dx=0\)
c) \(\int\limits^{\dfrac{1}{2}}_{-\dfrac{1}{2}}\ln\dfrac{1-x}{1+x}dx=0\)
d) \(\int\limits^2_0\left(\dfrac{1}{1+x+x^2+x^3}+1\right)dx=0\)
Tính các tích phân sau bằng phương pháp đổi biến số :
a) intlimits^2_1xleft(1-xright)^5dx (đặt t1-x)
b) intlimits^{ln2}_0sqrt{e^x-1}dx (đặt tsqrt{e^x-1})
c) intlimits^9_1xsqrt[3]{1-x}dx (đặt tsqrt[3]{1-x} )
d) intlimits^1_{-1}dfrac{2x+1}{sqrt{x^2+x+1}}dx (đặt usqrt{x^2+x+1})
e) intlimits^2_1dfrac{sqrt{1+x^2}}{x^4}dx (đặt tdfrac{1}{x} )
Đọc tiếp
Tính các tích phân sau bằng phương pháp đổi biến số :
a) \(\int\limits^2_1x\left(1-x\right)^5dx\) (đặt \(t=1-x\))
b) \(\int\limits^{\ln2}_0\sqrt{e^x-1}dx\) (đặt \(t=\sqrt{e^x-1}\))
c) \(\int\limits^9_1x\sqrt[3]{1-x}dx\) (đặt \(t=\sqrt[3]{1-x}\) )
d) \(\int\limits^1_{-1}\dfrac{2x+1}{\sqrt{x^2+x+1}}dx\) (đặt \(u=\sqrt{x^2+x+1}\))
e) \(\int\limits^2_1\dfrac{\sqrt{1+x^2}}{x^4}dx\) (đặt \(t=\dfrac{1}{x}\) )