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Integrate the term sec^{2}ax with respect to x.

Option: 1

\frac{1}{a}\ tan\ ax+C


Option: 2

-\frac{1}{a}\ tan\ ax+C


Option: 3

tan\ ax+C


Option: 4

-tan\ ax+C


Answers (1)

best_answer

Given integral,
\int sec^{2}ax\ dx
Using the substitution method,
Let’s take,
ax=t\Rightarrow a\ dx=dt
Therefore,
\int sec^{2}ax\ dx=\frac{1}{a}\int sec^{2}t\ dt
\int sec^{2}ax\ dx=\frac{1}{a}\ tan\ t+C
\int sec^{2}ax\ dx=\frac{1}{a}\ tan\ ax+C

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