Final answer to the problem
$\frac{_0^a\arctan\left(\frac{x}{a}\right)}{a}+C_0$
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Step-by-step Solution
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1
The integral of a function times a constant ($_0^a$) is equal to the constant times the integral of the function
$_0^a\int\frac{1}{a^2+x^2}dx$
Learn how to solve integrals of rational functions problems step by step online.
$_0^a\int\frac{1}{a^2+x^2}dx$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((_0^a)/(a^2+x^2))dx. The integral of a function times a constant (_0^a) is equal to the constant times the integral of the function. Factor the integral's denominator by a^2. Simplify the expression inside the integral. Solve the integral applying the substitution u^2=\frac{x^2}{a^2}. Then, take the square root of both sides, simplifying we have.
Final answer to the problem
$\frac{_0^a\arctan\left(\frac{x}{a}\right)}{a}+C_0$