int dx/(sin2x+tan2x)Can't use trig substitutions 114=Sdxsin²x+tan² x

Answered: int dx/(sin2x+tan2x) Can't use trig…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

int dx/(sin²x+tan²x)

Can't use trig substitutions

Expert Solution

Step 1

What is Indefinite Integration:

The integration of a function without any constraints is known as an indefinite integral. Integration is the opposite of differentiation and is sometimes referred to as the function's antiderivative. The indefinite integral is a crucial concept in calculus, and when limiting points are applied, they are transformed into definite integrals. In order to obtain the area bounded by the curve with respect to one of the coordinate axes, integration is defined for a function f(x).

Given:

Given integral is $\int \frac{d x}{\sin^{2} x + \tan^{2} x}$ .

To Determine:

We determine the integral.