Final Answer
Step-by-step Solution
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Apply the trigonometric identity: $\cos\left(\theta \right)^2$$=\frac{1+\cos\left(2\theta \right)}{2}$
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$\int x\frac{1+\cos\left(2x\right)}{2}dx$
Learn how to solve problems step by step online. Find the integral int(xcos(x)^2)dx. Apply the trigonometric identity: \cos\left(\theta \right)^2=\frac{1+\cos\left(2\theta \right)}{2}. Multiplying the fraction by x. Take the constant \frac{1}{2} out of the integral. We can solve the integral \int x\left(1+\cos\left(2x\right)\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 2x it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.