3. Arrange in descending order :
(a) 2/2/3, 2/2/7,2/1/14 , 2/1/6
this is mixed fraction question remember
Answers
Step-by-step explanation:
Step-by-step explanation:
Step-by-step explanation:
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☘℘ɧεŋσɱεŋศɭ☘
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❥Question᎓
integrate the function :
\frac{1}{x + xlogx}
x+xlogx
1
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꧁Answer꧂
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⟹ \frac{1}{x + xlogx} = \frac{1}{x(1 + logx)}⟹
x+xlogx
1
=
x(1+logx)
1
Let 1+logx=t
Differentiating both sides w.r.t.x
⟹ 0 + \frac{1}{x} = \frac{dt}{dx}⟹0+
x
1
=
dx
dt
⟹ \frac{1}{x} = \frac{dt}{dx}⟹
x
1
=
dx
dt
dx = xdtdx=xdt
Integrating function:-
⟹∫ \frac{1}{x + xlogx} dx = ∫ \frac{1}{x(1 + logx)} dx⟹∫
x+xlogx
1
dx=∫
x(1+logx)
1
dx
Putting 1+logx & dx =xdt
= ∫ \frac{1}{x(t)} dt \times x = ∫ \frac{1}{t} dt=∫
x(t)
1
dt×x=∫
t
1
dt
= log |t| + c=log∣t∣+c
Put t=1+logx
= log |1 + logx| + c=log∣1+logx∣+c
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