Evaluate the following definite integrals using the fundamental theorem of calculus: ∫(2+3)sec^2(x)dx from 1 to tan^2(x) and ∫(1/(x + 1))^2dx from 2 to 1.
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It seems like there are some typos in the given integral. I assume the correct integral is: $$\int_{0}^{2} \frac{\sec^2{x}}{\sqrt{1 - \tan^2{x}}} dx$$ Now, let's make a substitution. We know that $\sec^2{x} = 1 + \tan^2{x}$. Let's substitute $u = \tan{x}$, so Show more…
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