Final answer to the problem
$-\ln\left|\frac{2}{\sqrt{2^2+4}}\right|- -\ln\left|\frac{2}{\sqrt{{\left(-1\right)}^2+4}}\right|$
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Step-by-step Solution
Learn how to solve integral calculus problems step by step online. Integrate the function x/(x^2+4) from -1 to 2. We can solve the integral \int\frac{x}{x^2+4}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get. The integral of the tangent function is given by the following formula, \displaystyle\int\tan(x)dx=-\ln(\cos(x)).
Final answer to the problem
$-\ln\left|\frac{2}{\sqrt{2^2+4}}\right|- -\ln\left|\frac{2}{\sqrt{{\left(-1\right)}^2+4}}\right|$
Exact Numeric Answer
$0.235002$
