defence exam ITBP (Telecommunication) Head Constable Mock Test 2024 Mathematics Integral Calculus Indefinite Integrals
The value of \(\smallint \frac{{{e^x}}}{{{e^{2x}} - 4}}dx\) will be ______, where C is an arbitrary constant.
1
\(\frac{1}{2}\log \left| {\frac{{{e^x} + 1}}{{{e^x} - 1}}} \right| + C\)
2
\(\frac{1}{3}\log \left| {\frac{{{2e^x} - 1}}{{{2e^x} + 1}}} \right| + C\)
3
\(\frac{1}{4}\log \left| {\frac{{{e^x} - 2}}{{{e^x} + 2}}} \right| + C\)
4
\(\frac{1}{2}\log \left| {\frac{{{e^{2x}} + 2}}{{{e^{2x}} - 2}}} \right| + C\)