\(I=\int\dfrac{\left(\sqrt{x+1}+\sqrt{x}\right)dx}{x+1-x}=\int\sqrt{x+1}dx+\int\sqrt{x}dx\)
Xet \(I_1=\int\sqrt{x+1}dx\)
\(t=x+1\Rightarrow dt=dx\Rightarrow I_1=\int\sqrt{t}.dt=\dfrac{2}{3}\left(x+1\right)^{\dfrac{3}{2}}+C\)
\(\Rightarrow I=\dfrac{2}{3}\left(x+1\right)^{\dfrac{3}{2}}+\dfrac{2}{3}x^{\dfrac{3}{2}}+C\)
P/s: Bạn tự thay cận vô ạ
\(I=\int_1^2\dfrac{dx}{\left(x+1\right)\sqrt{x}+x\sqrt{x+1}}\)
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.\(\int\limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}}\sin x\sqrt{3+\cos^6x}dx\)
1/ I=\(\int_{-2}^2\left|x^2-1\right|dx\)
2/ I= \(\int_1^e\sqrt{x}.lnxdx\)
3/ I= \(\int_0^{\dfrac{\pi}{2}}\left(e^{sinx}+cosx\right)cosxdx\)
4/ I= \(\int_0^{\dfrac{pi}{2}}\dfrac{sin2x}{\sqrt{cos^2x+4sin^2x}}dx\)
5/ I= \(\int_0^{\dfrac{\pi}{4}}\sqrt{2}cos\sqrt{x}dx\)
6/ I= \(\int_1^{\sqrt{e}}\dfrac{1}{x\sqrt{1-ln^2x}}dx\)
7/ I= \(\int_{-\dfrac{\pi}{4}}^{\dfrac{\pi}{4}}\dfrac{sin^6x+cos^6x}{6^x+1}dx\)
Tính (trình bày cách giải ln nka):
a) \(\int_{\dfrac{\pi}{6}}^{\dfrac{\pi}{3}}\dfrac{1}{cos^4x}dx\)
b) \(\int_0^1\dfrac{\left(x+1\right)^2}{x^2+1}dx\)
c)\(\int_1^2\dfrac{x^2+2lnx}{x}dx\)
d) \(\int_1^2\dfrac{x^2+3x+1}{x^2+x}dx\)
e) \(\int_0^33x\left(x+\sqrt{x^2+16}\right)dx\)
a) I= \(\int_{-1}^0\) \(x^3\sqrt{x+1}dx\)
b) \(I=2\int^1_0\)\(\dfrac{x^2dx}{\left(x+1\right)\sqrt{x+1}}\)
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) \(\int\dfrac{\sqrt{x^2-9}}{x^3}dx\)
I=\(\int_0^3\) \(\dfrac{2x^2+x-1}{\sqrt{x+1}}dx\)
\(\int_0^m\left|\dfrac{x^2}{m}-\sqrt{mx}\right|dx\)=3
Giải bài này giúp mình với
Mọi người ơi , giúp e tính tích phân bất định với ạ ! Cảm ơn m.n ạ !
a.\(\int\frac{x+6}{\sqrt{x^2-2x+10}}dx\)
b.\(\int\frac{x}{\sqrt{3-2x-x^2}}dx\)
c.\(\int\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}dx\)
d,\(\int\frac{dx}{1+tanx}\)
e.\(\int tan^3xdx\)
f. \(\int cos^3xdx\)
g. \(\int sin^2x.cos^3xdx\)
h. \(\int sinx.cos2xdx\)
i. \(\int\frac{sin2x}{1+cos^2x}dx\)
