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$\int \frac{d x}{(\sin x)(\cos x)}$ is equal to
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2697 Upvotes
Verified Answer
The correct answer is:
$\log |\tan x|+c$
$$
\text { Let } \begin{aligned}
I & =\int \frac{d x}{\sin x \cos x} \\
I & =\int \frac{\sec ^2 x d x}{\tan x}
\end{aligned}
$$
Put $\tan x=t$
$$
\begin{array}{ll}
\Rightarrow & \sec ^2 x d x=d t \\
\therefore & I=\int \frac{d t}{t}=\log t+c \\
& I=\log |\tan x|+c
\end{array}
$$
\text { Let } \begin{aligned}
I & =\int \frac{d x}{\sin x \cos x} \\
I & =\int \frac{\sec ^2 x d x}{\tan x}
\end{aligned}
$$
Put $\tan x=t$
$$
\begin{array}{ll}
\Rightarrow & \sec ^2 x d x=d t \\
\therefore & I=\int \frac{d t}{t}=\log t+c \\
& I=\log |\tan x|+c
\end{array}
$$
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