Tinh tich phan:

$I=\int\limits_{1}^{4} \frac{xlnx}{(x^2+1)^2}dx$

Goi  $z=x+yi      (x,y\in R)$

        $\overline{z}=x-yi $

Ta co:  $|z+\overline{z}+5|=6 $

$\Leftrightarrow |x+yi+x-yi+5|=6$

$\Leftrightarrow |2x+5|=6$

$\Leftrightarrow (2x+5)^2=36$

den day ban lam not nhe

Tim phan thuc va phan ao cua so phuc sau:

$(\sqrt{3}+i)^{2014}$

Tim phan thuc va phan ao cua cac so phuc sau:

1)    $\frac{3-i}{1+2i}+4-3i$

2)    $\frac{(3-2i)[(4+3i)-(1+2i)]}{5-4i}$

3)   $(\sqrt{3}+I)^{2014}$

Goi $z = a+bi  (a,b\in R)$

$z^2=a^2-b^2+2abi$

$|z|= \sqrt{a^2+b^2}$

Thay vao cai ban dau roi tu tinh nhe

Cho so duong  $a,b,c $  thoa man  $a^2+b^2+c^2=3$ .  Chung minh rang:

$\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}\geq \frac{4}{a^2+7}+\frac{4}{b^2+7}+\frac{4}{c^2+7}$

Giai Phuong trinh :

$2cosx+\frac{1}{3}cos^2(x+7\Pi )=\frac{8}{3}+sin2(x-\Pi )+3cos(x+\frac{25\Pi }{2})+\frac{1}{3}sin^2x$

Cho ham so :  $y=x^3-3x^2+1$

Tim m de duong thang di qua diem   $A(-1;-3)$  co he so goc m cat (C) tai 3 diem phan biet cach deu nhau

Giai Phuong trinh

                 $sinx+1=\frac{3cos2x-5}{2cosx-4}$

Giai Phuong trinh : 

$2cosx+\frac{1}{3}\cos^2(x+7\Pi )=\frac{8}{3}+\sin 2(x-\Pi )+3\cos \left ( x+\frac{25\Pi }{2} \right )+\frac{1}{3}\sin^2 x$