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Chapter 5: Q 35. (page 452)

Solve the following integral.
$鈭� c s c^{4} x d x$

Short Answer

Expert verified

Answer is $\begin{array}{rcl} \frac{- c o t^{3} x}{3} - c o t x + C \end{array}$

Step by step solution

01

Step 1. Given information

An integral is $鈭� c s c^{4} x d x$

02

Step 2. Explanation

$\begin{array}{rcl} 鈭� c s c^{4} x d x & = & 鈭� c s c^{2} x c s c^{2} x d x \\ = & 鈭� (1 + c o t^{2} x) c s c^{2} x d x \end{array}$

Let $u = c o t x$

$\begin{array}{rcl} 鈭� c s c^{4} x d x & = & - 鈭� u^{2} + 1 d u \\ = & \frac{- u^{3}}{3} - u + C \\ = & \frac{- c o t^{3} x}{3} - c o t x + C \end{array}$

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Most popular questions from this chapter

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