Math, asked by siddhu3333, 6 months ago

(dy/dx)= y(y^4+1)/[2x(y^4-1)]

Answers

Answered by Anonymous
271

Step-by-step explanation:

\huge\mathfrak\green{\bold{\underline{☘{ ℘ɧεŋσɱεŋศɭ}☘}}}

\red{\bold{\underline{\underline{❥Question᎓}}}}integrate the function :

 \frac{1}{x + xlogx}

\huge\tt\underline\pink{꧁Answer꧂</p><p> }

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⟹ \frac{1}{x + xlogx}  =  \frac{1}{x(1 + logx)} </p><p>

Let 1+logx=t

Differentiating both sides w.r.t.x

⟹</p><p>0 +  \frac{1}{x}  =  \frac{dt}{dx}

⟹</p><p> \frac{1}{x}  =  \frac{dt}{dx}

dx = xdt

Integrating function:-

⟹∫ \frac{1}{x + xlogx} dx = ∫ \frac{1}{x(1 + logx)} dx</p><p>

Putting 1+logx & dx =xdt

 = ∫ \frac{1}{x(t)} dt \times x = ∫ \frac{1}{t} dt

 = log |t|  + c

Put t=1+logx

 = log |1 + logx|  + c

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