IT: Answer words. the following question a) How does the city with Where can one happiness ? in 100-180 the poet compaxe the life in the life in Q ting Island ? find long lasting 7( class 9)​

Answer:

भारत मेरा देश है और मै अपने राष्ट्र से बहुत प्यार करता हूं। हम सभी को अपनी मातृभूमि पसंद है और भारत मेरी मातृभूमि है, इसलिए मेरे दिल मे इसके लिए एक विशेष स्थान है। भारत एक बहु-सांस्कृतिक परिवार है, जहां आप विभिन्न प्रकार के लोगों, संस्कृतियों, परंपराओं, धर्मो के साथ-साथ कई भाषाओं को एक साथ पा सकते है।

Explanation:

Answer:

[tex]\qquad\boxed{ \sf{ \:\sf \:\displaystyle\int\sf \dfrac{1}{x \sqrt{ {x}^{4} - 1} } \: dx \: = \: \dfrac{1}{2} {tan}^{ - 1} \sqrt{ {x}^{4} - 1 } + c \: }}\\ \\ [/tex]

Step-by-step explanation:

Given integral is

[tex]\sf \:\displaystyle\int\sf \dfrac{1}{x \sqrt{ {x}^{4} - 1} } \: dx \\ \\ [/tex]

can be rewritten as

[tex]\sf \: = \: \displaystyle\int\sf \dfrac{ {4x}^{3} }{ {4x}^{3} \times x \sqrt{ {x}^{4} - 1} } \: dx \\ \\ [/tex]

[tex]\sf \: = \: \dfrac{1}{4} \displaystyle\int\sf \dfrac{ {4x}^{3} }{ {x}^{4} \sqrt{ {x}^{4} - 1} } \: dx \\ \\ [/tex]

Now, to evaluate this integral, we substitute

[tex]\sf \: \sqrt{ {x}^{4} - 1} = y \\ \\ [/tex]

[tex]\sf \: {x}^{4} - 1 = {y}^{2} \\ \\ [/tex]

[tex]\sf\implies \sf \: {x}^{4} = {y}^{2} + 1 \\ \\ [/tex]

[tex]\sf\implies \sf \: 4{x}^{3} \: dx = 2y \: dy \\ \\ [/tex]

So, on substituting the values, we get

[tex]\sf \: = \: \dfrac{1}{4} \displaystyle\int\sf \dfrac{ 2y }{( {y}^{2} + 1) y } \: dy\\ \\ [/tex]

[tex]\sf \: = \: \dfrac{1}{2} \displaystyle\int\sf \dfrac{1 }{ {y}^{2} + 1 } \: dy\\ \\ [/tex]

[tex]\sf \: = \: \dfrac{1}{2} {tan}^{ - 1}y + c \\ \\ [/tex]

[tex]\sf \: = \: \dfrac{1}{2} {tan}^{ - 1} \sqrt{ {x}^{4} - 1 } + c \\ \\ [/tex]

Hence,

[tex]\sf\implies \boxed{ \sf{ \:\sf \:\displaystyle\int\sf \dfrac{1}{x \sqrt{ {x}^{4} - 1} } \: dx \: = \: \dfrac{1}{2} {tan}^{ - 1} \sqrt{ {x}^{4} - 1 } + c \: }}\\ \\ [/tex]

[tex]\rule{190pt}{2pt}[/tex]

Additional Information

[tex]\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c} \bf f(x) & \bf \displaystyle \int \rm \:f(x) \: dx\\ \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf k & \sf kx + c \\ \\ \sf sinx & \sf - \: cosx+ c \\ \\ \sf cosx & \sf \: sinx + c\\ \\ \sf {sec}^{2} x & \sf tanx + c\\ \\ \sf {cosec}^{2}x & \sf - cotx+ c \\ \\ \sf secx \: tanx & \sf secx + c\\ \\ \sf cosecx \: cotx& \sf - \: cosecx + c\\ \\ \sf tanx & \sf logsecx + c\\ \\ \sf \dfrac{1}{x} & \sf logx+ c\\ \\ \sf {e}^{x} & \sf {e}^{x} + c\end{array}} \\ \end{gathered}\end{gathered}[/tex]

Answer:

Question is not clear . please retype it some other way

Answer:

A turing machine consists of a tape of infinite length on which read and writes operation can be performed. The tape consists of infinite cells on which each cell either contains input symbol or a special symbol called blank. It also consists of a head pointer which points to cell currently being read and it can move in both directions.

Explanation:

I don't know whether it is correct or not

If it is correct then,

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