trigonometric integrals

Question

The integral ∫cos²(x) dx can be evaluated using

RankGuru · Accepted Answer

1. **Trig Identity Application**: Standard power-reduction identity is $\cos^2 x = \frac{1 + \cos(2x)}{2}$.
2. **Transform Integral**: $\int \cos^2 x \, dx = \int \frac{1 + \cos(2x)}{2} \, dx$.
3. **Evaluate Separately**:
   - $\int \frac{1}{2} dx = \frac{x}{2}$
   - $\int \frac{\cos(2x)}{2} dx = \frac{\sin(2x)}{4}$
4. **Consolidated Result**: $\frac{x}{2} + \frac{\sin 2x}{4} + C$.

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trigonometric integrals

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