Answered: csc'x + 1 dx csc x

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Calculus

csc'x + 1 dx csc x

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter1: Equations And Inequalities

Section1.CT: Chapter Test

Problem 5CT: Solve for x: z=x.

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Question

Determine the following indefinite integral. Check your work by differentiation.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

Expert Solution

Step 1

The Given integral is $\int \frac{c s c^{3} x + 1}{c s c x} d x$ .

$\begin{array}{rcl} \int \frac{c s c^{3} x + 1}{c s c x} d x & = & \int \frac{c s c^{3} x}{c s c x} d x + \int \frac{1}{c s c x} d x \\ = & \int c s c^{2} x d x + \int \frac{1}{c s c x} d x \\ = & - c o t x + \int \sin x d x \end{array}$

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