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Evaluate the integral: ∫ (1/(x^2 + 1)) dx
Evaluate the integral: ∫ (1/(x^2 + 1)) dx
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Practice Questions
1 question
Q1
Evaluate the integral: ∫ (1/(x^2 + 1)) dx
tan^(-1)(x) + C
sin^(-1)(x) + C
ln
x
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The integral of 1/(x^2 + 1) is tan^(-1)(x) + C.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate the integral: ∫ (1/(x^2 + 1)) dx
Solution:
The integral of 1/(x^2 + 1) is tan^(-1)(x) + C.
Steps: 5
Show Steps
Step 1: Identify the integral you need to evaluate, which is ∫ (1/(x^2 + 1)) dx.
Step 2: Recognize that the function 1/(x^2 + 1) is a standard integral that corresponds to the derivative of the arctangent function.
Step 3: Recall that the derivative of tan^(-1)(x) is 1/(x^2 + 1).
Step 4: Therefore, the integral ∫ (1/(x^2 + 1)) dx equals tan^(-1)(x) plus a constant of integration, C.
Step 5: Write the final answer as tan^(-1)(x) + C.
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