Question

\(\displaystyle \int \sec^{2}4x\,dx=\) ?

• A. \(\tan4x+k\)
• B. \(\dfrac14\tan4x+k\)
• C. \(4\tan4x+k\)
• D. \(8\tan4x+k\)

Hint:

Differentiate to verify: $\left(\frac{1}{a}\tan ax\right)'=\sec^{2}ax$.

Answer 1

The Correct Option is B

\(\displaystyle \int \sec^{2}(ax)\,dx=\frac{1}{a}\tan(ax)+C\). With \(a=4\), answer is \(\frac14\tan4x+k\).