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Find the integrals \int \frac{\sin (lnx )}{x}dx

  • Option 1)

    \cos (lnx )+C

  • Option 2)

    - \cos (lnx )+ C

  • Option 3)

    \sin (lnx )+ C

  • Option 4)

    -\sin (lnx )+ C

Answers (1)

best_answer

As we have learned

Type of integration by substitution -

Integral of the functions containing functions of trigonometric functions 

\because \int sin f(x)\left f'(x) \right dx

\therefore \int sint dt = -cos t+c

ex:  \therefore \int sin\left ( ax+b \right )dx=\frac{-cos(ax+b)}{a}+c

- wherein

Let f(x)=t

\therefore f'(x)dx=dt

 

put (lnx) = t 

\Rightarrow \frac{dx}{x}= dt

I= \int (\sin t)dt = -\cos (lnx)+ C

 

 

 

 


Option 1)

\cos (lnx )+C

This is incorrect

Option 2)

- \cos (lnx )+ C

This is correct

Option 3)

\sin (lnx )+ C

This is incorrect

Option 4)

-\sin (lnx )+ C

This is incorrect

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