IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

sneha.bagri

$\int$ (4e^x + 6e^-x)/(9e^x - 4e^-x) equals????

plz giv ur xplanations.............

allamraju

Write the numerator as l(9e^x-4e^-x)+m(9e^x+4e^-x)=4e^x+6e^-x.solving for l,m by equating the coefficients,we get l=-19/36,m=35/36.Hence the integrand is

-19x/36+35/36ln(I9e^x-4e^-xI)

angel.angelina

$\int$ (4e^x+6/e^x)/9e^x+4/e^x)= $\int$ e^x(4+6/e^2x)/e^x(9+4/e^2x)= $\int$ (4e^2x+6)/(9e^2x+4)=4/18 $\int$ 18e^2x/(9e^2x+4) + 6 $\int$ 1/(9e^2x+4)=2/9log(9e^2x+4) +6 $\int$ 1/(3e^x)^2+2^2 proceed further & get ANSWER. RATE IF SATISFIED.

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Write the numerator as l(9ex-4e-x)+m(9ex+4e-x)=4ex+6e-x.solving for l,m by equating the coefficients,we get l=-19/36,m=35/36.Hence the integrand is

-19x/36+35/36ln(I9ex-4e-xI)

Write the numerator as l(9e^x-4e^-x)+m(9e^x+4e^-x)=4e^x+6e^-x.solving for l,m by equating the coefficients,we get l=-19/36,m=35/36.Hence the integrand is

-19x/36+35/36ln(I9e^x-4e^-xI)