Question

\(25\displaystyle \int \sec5x\,\tan5x\,dx=\) ?

• A. \(25\sec5x+k\)
• B. \(5\sec5x+k\)
• C. \(25\tan5x+k\)
• D. \(\sec5x+k\)

Hint:

When inside is $5x$, pull out $\frac{1}{5}$; outside constants multiply at the end.

Answer 1

The Correct Option is B

\(\displaystyle \int \sec u\,\tan u\,du=\sec u+C\). Let \(u=5x\Rightarrow du=5\,dx\): \[ \int \sec5x\,\tan5x\,dx=\frac{1}{5}\sec5x+k. \] Multiply by \(25\Rightarrow 5\sec5x+k\).