Math Problem Statement
(1/(1+16x^2))dx
Solution
We are tasked with evaluating the integral:
Step 1: Simplify the Integral
We can try to simplify this expression. One approach is to separate the integral into a more manageable form by rewriting the numerator and the denominator in a way that makes integration simpler.
Step 2: Substitution
A good substitution here is to let:
Thus, differentiating with respect to :
or equivalently:
Step 3: Rewrite the Integral
Now, we can rewrite the integral in terms of . First, observe that:
Substitute this and into the original integral:
This is where the substitution leads to some simplifications.
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Math Problem Analysis
Mathematical Concepts
Integral Calculus
Substitution Method
Formulas
∫ f(u) du = F(u) + C (indefinite integral)
Substitution: u = 1 + 16x^2
Theorems
Substitution Rule in Integration
Suitable Grade Level
College-Level Calculus
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