x ( x tan - 1 x + ( ln x ) ( ln ( ln x ) ) ) + tan - 1 x ( x 3 + x ) ln x = f ( x ) + c where ' c ' is integration constant & f ( e ) = 0 Then [ lim x 1 + f ( x ) tan ( x 2 ) + 11 10 ] = _ _ _ _ _ , where [ . ] denotes GIF

Question

$\int \frac{x (x \tan^{- 1} x + (\ln x) (\ln (\ln x))) + \tan^{- 1} x}{(x^{3} + x) \ln x} = f (x) + c$ where $' c'$ is integration constant & $f (e) = 0$

Then $[\lim_{x \to 1^{+}} \frac{f (x)}{\tan (\frac{π x}{2})} + \frac{11}{10}] =_____,$ where $[.]$ denotes GIF

Smart Achievers · Accepted Answer

(2)

$Given$ $\int \tan^{- 1} x \cdot \frac{1}{x (\ln x)} + \frac{1}{1 + x^{2}} \cdot \ln (\ln x)$

$∴$ $f (x) = (\tan^{- 1} x) \ln (\ln x)$

Solution

Q.
$\int \frac{x (x \tan^{- 1} x + (\ln x) (\ln (\ln x))) + \tan^{- 1} x}{(x^{3} + x) \ln x} = f (x) + c$ where $' c'$ is integration constant & $f (e) = 0$

Then $[\lim_{x \to 1^{+}} \frac{f (x)}{\tan (\frac{π x}{2})} + \frac{11}{10}] =_____,$ where $[.]$ denotes GIF

1 2

2 1

3 0

4 - 1

Ans.
(2)

$Given$ $\int \tan^{- 1} x \cdot \frac{1}{x (\ln x)} + \frac{1}{1 + x^{2}} \cdot \ln (\ln x)$

$∴$ $f (x) = (\tan^{- 1} x) \ln (\ln x)$

Want Us to Email you About Special Offers & Updates?

Solution

Q. ∫x(xtan-1x+(lnx)(ln(lnx)))+tan-1x(x3+x)lnx=f(x)+c where 'c' is integration constant & f(e)=0 Then [limx→1+f(x)tan(πx2)+1110]=_____, where [.] denotes GIF

1 2

2 1

3 0

4 - 1

Ans. (2) Given ∫tan-1x·1x(lnx)+11+x2·ln(lnx) ∴ f(x)=(tan-1x)ln(lnx)

Want Us to Email you About Special Offers & Updates?

Q.
$\int \frac{x (x \tan^{- 1} x + (\ln x) (\ln (\ln x))) + \tan^{- 1} x}{(x^{3} + x) \ln x} = f (x) + c$ where $' c'$ is integration constant & $f (e) = 0$

Then $[\lim_{x \to 1^{+}} \frac{f (x)}{\tan (\frac{π x}{2})} + \frac{11}{10}] =_____,$ where $[.]$ denotes GIF

Ans.
(2)

$Given$ $\int \tan^{- 1} x \cdot \frac{1}{x (\ln x)} + \frac{1}{1 + x^{2}} \cdot \ln (\ln x)$

$∴$ $f (x) = (\tan^{- 1} x) \ln (\ln x)$