Calculus Examples

$\int \frac{1}{\cot (u)} d u$

Step 1

Simplify.

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Step 1.1

Rewrite $\cot (u)$ in terms of sines and cosines.

$\int \frac{1}{\frac{\cos (u)}{\sin (u)}} d u$

Step 1.2

Multiply by the reciprocal of the fraction to divide by $\frac{\cos (u)}{\sin (u)}$ .

$\int \frac{\sin (u)}{\cos (u)} d u$

Step 1.3

Convert from $\frac{\sin (u)}{\cos (u)}$ to $\tan (u)$ .

$\int \tan (u) d u$

Step 2

The integral of $\tan (u)$ with respect to $u$ is $\ln (| \sec (u) |)$ .

$\ln (| \sec (u) |) + C$