Evaluate the integrals $$ \int_{0}^{\pi / 3}(\cos x+\sec x)^{2} d x $$
Added by Juan Antonio M.
Step 1
First, we can rewrite the integral using the identity $\sec x = \frac{1}{\cos x}$:$$\int_{0}^{\pi / 3}(\cos x + \frac{1}{\cos x})^2 dx$$ Now, let's expand the square:$$\int_{0}^{\pi / 3}(\cos^2 x + 2 + \frac{1}{\cos^2 x}) dx$$ We can split the integral into three Show more…
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