rock.freak667 said:try substituting u=x2+1, du=?
The general approach to integrating x/(x^2+1)dx is to use the substitution method. This involves substituting the expression inside the parentheses with a new variable, u, and rewriting the integral in terms of u. This allows for the use of known integration techniques, such as the power rule or integration by parts.
The most common substitution for x/(x^2+1)dx is u = x^2+1. This allows for the integral to be rewritten as ∫(1/u)du, which can be easily integrated using the natural logarithm function.
Yes, x/(x^2+1)dx can also be integrated using trigonometric substitutions. One possible substitution is u = tan(x), which leads to the integral becoming ∫(1/u^2+1)du. This can be integrated using the inverse tangent function.
No, the integral x/(x^2+1)dx cannot be solved without substitution. This is because the expression x^2+1 does not have a known antiderivative, making it impossible to use basic integration techniques.
Yes, in addition to substitution and trigonometric substitutions, x/(x^2+1)dx can also be integrated using partial fractions. This involves breaking the fraction into smaller, simpler fractions and then integrating each term separately. However, this method can be more complex and time-consuming compared to the substitution method.