\( f(x)=\int \frac{2 x}{\left(x^{2}+1\right)\left(x^{2}+3\right)} d x \) if \( f(3)=\frac{1}{2}[\ln 5-\ln 6] \), then \( f(4) \) is:

\( \frac{1}{2}[\ln 19-\ln 17] \)

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

f(x)=\int \frac{2 x}{\left(x^{2}+1\right)\left(x^{2}+3\right)} d x

f(3)=\frac{1}{2}[\ln 5-\ln 6]

, then

f(4)

is:

View answer and explanation

Correct option: A

\frac{1}{2}[\ln 17-\ln 19]

Option A (

\frac{{1}}{{2}}[\ln 17 - \ln 19]

) is correct because it is the result of evaluating the definite integral with the given condition.

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