Math Problem Statement

Solve

Solve the integral of dx divided by sin(x) * cos^2(x).

Solution

The integral in the image is:

∫dxsin⁡(x)⋅cos⁡2(x)\int \frac{dx}{\sin(x) \cdot \cos^2(x)}

To solve this, we can use trigonometric identities and substitution:

Step 1: Use a trigonometric identity

We can express the integrand in terms of tangent: [ \cos^2(x) = \frac{1}{1 + \tan^2(x)} \quad \text{and} \quad \sin(x) = 2\tan(x)

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Math Problem Analysis

Mathematical Concepts

Calculus
Trigonometric Integration
Substitution Method

Formulas

cos^2(x) = 1 - sin^2(x)
Integral identity for tangent: ∫tan(x) dx = ln|sec(x)|

Theorems

Trigonometric Identity Theorem
Substitution in Integration

Suitable Grade Level

Undergraduate (Calculus Level)

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