Final Answer
$\ln\left(\sqrt{x^2+1}\right)+C_0$
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Step-by-step Solution
Problem to solve:
$\int\frac{x^{\left(2-1\right)}}{x^2+1}dx$
Specify the solving method
1
Simplify the expression inside the integral
$\int\frac{x}{x^2+1}dx$
Learn how to solve integrals of rational functions problems step by step online.
$\int\frac{x}{x^2+1}dx$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^(2-1))/(x^2+1))dx. Simplify the expression inside the integral. We can solve the integral \int\frac{x}{x^2+1}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.
Final Answer
$\ln\left(\sqrt{x^2+1}\right)+C_0$