CBSE 2024 · Region 2 · Set 1 · Q24 · 2 marks
Find : \[\int \frac{e^{4 x}-1}{e^{4 x}+1} d x \]
Marking-scheme solution
Dividing numerator and denominator by \(\displaystyle e^{2x}\):
\[\begin{aligned}
\int \frac{e^{4x}-1}{e^{4x}+1}\,dx &= \int \frac{e^{2x}-e^{-2x}}{e^{2x}+e^{-2x}}\,dx \\
&= \frac{1}{2}\int \frac{2\left(e^{2x}-e^{-2x}\right)}{e^{2x}+e^{-2x}}\,dx \\
&= \frac{1}{2}\log\left|e^{2x}+e^{-2x}\right| + C
\end{aligned}
\]
IntegralsMethods of IntegrationApplyvery_short_answermedium
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CBSE Class 12 Mathematics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.