- #1
- 11
- 0
im having a bit of trouble, can anyone help me integrate arctan(1/x) using integration by parts?
thanks
thanks
The formula for integrating arctan(1/x) with Integration by Parts is ∫arctan(1/x)dx = xarctan(1/x) - ∫(x/(1+x^2))dx.
The steps for integrating arctan(1/x) with Integration by Parts are as follows:
1. Identify u and dv in the given integral.
2. Use the formula ∫udv = uv - ∫vdu to rewrite the integral.
3. Integrate v and differentiate u.
4. Substitute the values of u, v, and ∫vdu into the formula.
5. Simplify the resulting integral and solve for the final answer.
The value of arctan(1/x) is the angle whose tangent is equal to 1/x. It can also be represented as the inverse tangent of 1/x.
Some possible substitutions for arctan(1/x) are:
1. x = tanθ
2. u = 1/x
3. x = 1/tanθ
4. u = arctan(1/x)
You can check your answer by differentiating the final result and seeing if it matches the original integrand. You can also use online integration calculators or ask a math tutor for assistance.