Question

What is \(\int \cos^2 x\,dx\)?

Options

• \(x+\frac{1}{4}\sin 2x+\text{C}\)

• \(\frac{x}{2}+\frac{1}{2}\sin 2x+\text{C}\)

• \(\frac{x}{2}-\frac{1}{4}\sin 2x+\text{C}\)

• \(\frac{x}{2}+\frac{1}{4}\sin 2x+\text{C}\)

Answer 1

Use \(\cos^2 x=\frac{1+\cos 2x}{2}\), then integrate each term. Since \(\int\cos 2x\,dx=\frac{1}{2}\sin 2x\), the result is \(\frac{x}{2}+\frac{1}{4}\sin 2x+\text{C}\).