Question:
\(25\displaystyle \int \sec5x\,\tan5x\,dx=\) ?
\(25\displaystyle \int \sec5x\,\tan5x\,dx=\) ?
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When inside is $5x$, pull out $\frac{1}{5}$; outside constants multiply at the end.
Updated On: Oct 17, 2025
- \(25\sec5x+k\)
- \(5\sec5x+k\)
- \(25\tan5x+k\)
- \(\sec5x+k\)
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The Correct Option is B
Solution and Explanation
\(\displaystyle \int \sec u\,\tan u\,du=\sec u+C\).
Let \(u=5x\Rightarrow du=5\,dx\):
\[
\int \sec5x\,\tan5x\,dx=\frac{1}{5}\sec5x+k.
\]
Multiply by \(25\Rightarrow 5\sec5x+k\).
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