a. \(\int cosx.sin^3xdx=\int sin^3x.d\left(sinx\right)=\dfrac{sin^4x}{4}+C\)

b. \(\int sinx.cos^5xdx=-\int cos^5x.d\left(cosx\right)=-\dfrac{cos^6x}{6}+C\)

c. \(\int x\left(x^2+1\right)^{10}dx=\dfrac{1}{2}\int\left(x^2+1\right)^{10}d\left(x^2+1\right)=\dfrac{\left(x^2+1\right)^{11}}{22}+C\)

d. \(\int x\left(2-x\right)^5dx\)

Đặt \(\left\{{}\begin{matrix}u=x\\dv=\left(2-x\right)^5dx\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}du=dx\\v=-\dfrac{1}{6}\left(2-x\right)^6\end{matrix}\right.\)

\(\Rightarrow I=-\dfrac{x\left(2-x\right)^6}{6}+\dfrac{1}{6}\int\limits\left(2-x\right)^6dx=-\dfrac{x\left(2-x\right)^6}{6}+\dfrac{1}{42}\left(x-2\right)^7+C\)

e.

\(I=\int\dfrac{2x+1}{\left(x-3\right)^3}dx=\int\dfrac{2\left(x-3\right)+6}{\left(x-3\right)^3}dx=2\int\dfrac{dx}{\left(x-3\right)^2}+6\int\dfrac{dx}{\left(x-3\right)^3}\)

\(=-\dfrac{2}{x-3}-\dfrac{3}{\left(x-3\right)^2}+C\)

f.

\(I=\int\dfrac{\left(2x-1\right)^4}{\left(x+3\right)^6}dx=\int\dfrac{\left[2\left(x+3\right)-7\right]^4}{\left(x+3\right)^6}dx=\int\left(2-\dfrac{7}{x+3}\right)^4.\dfrac{1}{\left(x+3\right)^2}dx\)

Đặt \(2-\dfrac{7}{x+3}=u\Rightarrow du=\dfrac{7}{\left(x+3\right)^2}dx\Rightarrow\dfrac{1}{\left(x+3\right)^2}dx=\dfrac{1}{7}du\)

\(\Rightarrow I=\dfrac{1}{7}\int u^4du==\dfrac{1}{35}.u^5+C=\dfrac{1}{35}\left(2-\dfrac{7}{x+3}\right)^5+C\)

g.

\(I=\int x\sqrt{1-x}dx\)

Đặt \(\sqrt{1-x}=u\Rightarrow x=1-u^2\Rightarrow dx=-2u.du\)

\(I=\int\left(1-u^2\right).u.\left(-2u.du\right)=\int\left(2u^4-2u^2\right)du=\dfrac{2}{5}u^5-\dfrac{2}{3}u^3+C\)

\(=\dfrac{2}{5}\sqrt{\left(1-x\right)^5}-\dfrac{2}{3}\sqrt{\left(1-x\right)^3}+C\)

h.

\(I=\int\dfrac{\left(1-2e^x\right)e^x}{e^x+1}dx\)

Đặt \(e^x+1=u\Rightarrow e^xdx=du\)

\(I=\int\dfrac{\left(1-2\left(u-1\right)\right)}{u}du=\int\dfrac{3-2u}{u}du=\int\left(\dfrac{3}{u}-2\right)du=3lnu-2u+C\)

\(=3ln\left(e^x+1\right)-2\left(e^x+1\right)+C=3ln\left(e^x+1\right)-2e^x+C\)

i.

Đặt \(lnx=u\Rightarrow\dfrac{dx}{x}=du\)

\(I=\int\left(u^2-3u\right)du=\dfrac{u^3}{3}-\dfrac{3u^2}{2}+C=\dfrac{ln^3x}{3}=\dfrac{3ln^2x}{2}+C\)

giúp mik điiiiiiiii mad 

6:

1: BH=căn 15^2-12^2=9cm

BC=15^2/9=25cm

AC=căn 25^2-15^2=20cm

C ABC=15+20+25=60cm

XétΔHAB vuông tại H có sin BAH=BH/AB=9/15=3/5

nên góc BAH=37 độ

2: ΔABC vuông tại A có AH là đường cao

nên CA^2=CH*CB

ΔCAH vuông tại H có HF là đường cao

nên CF*CA=CA^2=CH*CB

3: Xét tứ giác AFHB có

HF//AB

góc AFH=90 độ

=>AFHB là hình thang vuông

Giúp mik vs mọi người đâu hết rùi😄😄😄

Câu 6.

a)Trong hai vật trên: quả cầu thép tỏa nhiệt, nước thu nhiệt.

b)Gọi nhiệt độ ban đầu hệ là \(t_0^oC\).

Nhiệt lượng quả cầu tỏa ra:

\(Q_{tỏa}=m_1c_1\left(t_1-t_0\right)=0,761\cdot460\cdot\left(100-t_0\right)\)

Nhiệt lượng nước thu vào:

\(Q_{thu}=m_2c_2\left(t_0-t_2\right)=0,5\cdot4200\cdot\left(t_0-40\right)J\)

Cân bằng nhiệt: \(Q_{tỏa}=Q_{thu}\)

\(\Rightarrow0,761\cdot460\cdot\left(100-t_0\right)=0,5\cdot4200\cdot\left(t_0-40\right)\)

\(\Rightarrow t_0=48,57^oC\)

Câu 7.

Gọi nhiệt độ của nước khi cân bằng là \(t^oC\).

Nhiệt lượng miếng nhôm tỏa ra:

\(Q_{tỏa}=m_1c_1\left(t_1-t\right)=0,5\cdot880\cdot\left(100-t\right)J\)

Nhiệt lượng nước thu vào:

\(Q_{thu}=m_2c_2\left(t-t_2\right)=0,8\cdot4200\cdot\left(t-20\right)J\)

Cân bằng nhiệt: \(Q_{tỏa}=Q_{thu}\)

\(\Rightarrow0,5\cdot880\cdot\left(100-t\right)=0,8\cdot4200\cdot\left(t-20\right)\)

\(\Rightarrow t=29,26^oC\)

Chọn D

\(AH=16\cdot2:8=4\left(cm\right)\)

Câu 1:

a: Xét ΔADC có ME//DC

nên \(\dfrac{AM}{MD}=\dfrac{AE}{EC}\)

b: Xét ΔCAB có EF//AB

nên \(\dfrac{CE}{EA}=\dfrac{CF}{FB}\)

=>\(\dfrac{AE}{EC}=\dfrac{BF}{FC}\)

c: ta có: \(\dfrac{AM}{MD}=\dfrac{AE}{EC}\)

\(\dfrac{AE}{EC}=\dfrac{BF}{FC}\)

Do đó: \(\dfrac{AM}{MD}=\dfrac{BF}{FC}\)

d: Ta có: \(\dfrac{AM}{MD}=\dfrac{BF}{FC}\)

=>\(\dfrac{AM+MD}{MD}=\dfrac{BF+FC}{FC}\)

=>\(\dfrac{AD}{MD}=\dfrac{BC}{FC}\)

=>\(\dfrac{DM}{DA}=\dfrac{CF}{CB}\)

Bài 2:

Xét ΔADC có OM//DC

nên \(\dfrac{OM}{DC}=\dfrac{AM}{AD}\)(1)

Xét ΔBDC có ON//DC

nên \(\dfrac{ON}{DC}=\dfrac{BN}{BC}\left(2\right)\)

Xét hình thang ABCD có MN//AB//CD

nên \(\dfrac{AM}{MD}=\dfrac{BN}{NC}\)

=>\(\dfrac{MD}{AM}=\dfrac{CN}{BN}\)

=>\(\dfrac{MD+AM}{AM}=\dfrac{CN+BN}{BN}\)

=>\(\dfrac{AD}{AM}=\dfrac{BC}{BN}\)

=>\(\dfrac{AM}{AD}=\dfrac{BN}{BC}\left(3\right)\)

Từ (1),(2),(3) suy ra OM=ON

a nha bn

how far is your village the city

a.to   b.from  c.in  d.for

lộn nha bn câu b  :D

My favorite sport is playing badminton. There are four reasons why I like it. Firstly, I can improve my health through playing it. I play it about 2 times every week. It makes me feel energetic everyday. Secondly, I enjoy the feeling that badminton flies in the air. I can change the movement direction of badminton without much effort and make opponent lose it. Thirdly, I can make many friends when I play badminton. I often play it with many kinds of persons. We can improve our skills with exercises. Also we talk about many interesting things when we have a break. Finally, playing badminton is not as intense as other sports such as basketball and soccer. It lessens the possibility of being hurt. So If you like playing badminton, please feel free to contact me. I think we can exchange experiences and make friends.

MY favourite sport is playing badminton.Badminton or Mark Bridge is used racquet sport played with two athletes (single game) or two pairs of athletes (doubles) players on the 2 halves of a rectangular field divided by a net in the middle. Players score points by bringing orb racket over the net and hit the ground with the other party in the courtyard of the opponents. Each side needs only one single touch to bring the bridge to the other side of the field. Hit the bridge ends when the ball hits the ground, or an error by the referee or linesman caught; no arbitration cases are due to players caught themselves, at any point in the globe are hitting plays.

There are a lot of kind of sports all over the world, but badminton is the one I like best. It's very easy to play badminton. 2 or 4 players will participate in this sport. They use a racket to hit the shuttlecock over the net. When the shuttlecock fall to the ground, the opposite player will get 1 point. If 1 player or 1 team get 21 points, they will win. Because of its ease, everyone can play it easily with a racket or a shuttlecock, even without a net. So I like badminton best.