Chapter 5: Q 12. (page 495)

Fill in the blanks to complete each of the following integration formulas.
$\int \cot x d x =_____$

Short Answer

Expert verified

The result is $\ln |\sin (x)| + C$ .

Step by step solution

Step 1. Given information.

Consider the given integration.

$\int \cot x d x$

Step 2. Find the integration.

Simplify the expression and find the integration.

$\int \cot x d x = \int \frac{\cos x}{\sin x} d x$

Put $\sin x = t$ and $d t = \cos x d x$ .

Substitute the above values in integration.

$\begin{array}{rcl} \int \frac{\cos x}{\sin x} d x & = & \int \frac{1}{t} d t \\ = & \ln |t| + C \\ = & \ln |\sin (x)| + C \end{array}$

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Fill in the blanks to complete each of the following integration formulas.
$\int \cot x d x =_____$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the integration.

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Fill in the blanks to complete each of the following integration formulas.∫cotxdx=_____

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the integration.

One App. One Place for Learning.

Most popular questions from this chapter

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Fill in the blanks to complete each of the following integration formulas.
$\int \cot x d x =_____$