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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int \large\frac{ 6 \cos (\log (3x)+1)}{7x} $$dx$

$(a)\;\frac{6}{7} \sin (\log (3n+1))+c \qquad(b)\;\frac{6}{7} \sin (\log (3n-1))+c \qquad(c)\;\cos (\log (3n+1))+c \qquad (d)\;None$
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1 Answer

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$\int \large\frac{ 6 \cos (\log (3x)+1)}{7x} $$dx$
=> $[\log (3x)+1]=t$
differentiate with respect to x
=> $x => \large\frac{1}{3x}$$ \times 3 dx =dt$
=> $ \large\frac{6}{7}$$ \int \cos t .dt$
=>$\large\frac{6}{7}$$ \sin (\log (3n+1))$$+c $
Hence a is the correct answer.
answered Dec 23, 2013 by meena.p
 
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