If $\smallint \,\,\frac{{4{e^x} + \,\,6{e^{ - x}}}}{{9{e^x} - \,\,4{e^{ - x}}}}\,\,dx = Ax + B\,\,\log \,\,\left( {9{e^{2x}} - \,\,4} \right) + C$, then

$A = - \,\,\frac{3}{2},\,\,\;B = \frac{{35}}{{36}},\;\,\,C = 0$

$A = \frac{{35}}{{36}},\;\,\,B = - \,\,\frac{3}{2},\;\,\,C \in R$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int \,\,\frac{{4{e^x} + \,\,6{e^{ - x}}}}{{9{e^x} - \,\,4{e^{ - x}}}}\,\,dx = Ax + B\,\,\log \,\,\left( {9{e^{2x}} - \,\,4} \right) + C

, then

View answer and explanation

Correct option: C

A = - \,\,\frac{3}{2},\;\,\,B = \frac{{35}}{{36}},\;\,\,C \in R

Option C (

A = - \,\frac{3}{2},\,\;B = \frac{{35}}{{36}},\,\;C \in R

) is correct because after integrating the given function and comparing with the given form, we find the values of A and B.