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Integrate 1/(x^2+1), correct answer is tan inverse x?
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Integrate 1/(x^2+1), correct answer is tan inverse x?
Integration of 1/(x^2 +1)
To integrate 1/(x^2 +1), we can use the substitution method of integration. Let u = x^2 +1. Then du/dx = 2x, or dx = du/(2x).
Substituting u and dx in the integral, we get:
∫ 1/(x^2 +1) dx = ∫ 1/u * du/(2x) = (1/2) ∫ du/u = (1/2) ln |u| + C
where C is the constant of integration.
Substituting back u = x^2 +1, we get:
∫ 1/(x^2 +1) dx = (1/2) ln |x^2 +1| + C
However, we can simplify this expression further by using the identity:
tan inverse x = 1/2 ln |(1+x)/(1-x)| + C
Therefore, the final answer for the integral is:
∫ 1/(x^2 +1) dx = tan inverse x + C
To integrate 1/(x^2 +1), we can use the substitution method of integration. Let u = x^2 +1. Then du/dx = 2x, or dx = du/(2x).
Substituting u and dx in the integral, we get:
∫ 1/(x^2 +1) dx = ∫ 1/u * du/(2x) = (1/2) ∫ du/u = (1/2) ln |u| + C
where C is the constant of integration.
Substituting back u = x^2 +1, we get:
∫ 1/(x^2 +1) dx = (1/2) ln |x^2 +1| + C
However, we can simplify this expression further by using the identity:
tan inverse x = 1/2 ln |(1+x)/(1-x)| + C
Therefore, the final answer for the integral is:
∫ 1/(x^2 +1) dx = tan inverse x + C
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Integrate 1/(x^2+1), correct answer is tan inverse x?
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Integrate 1/(x^2+1), correct answer is tan inverse x? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Integrate 1/(x^2+1), correct answer is tan inverse x? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Integrate 1/(x^2+1), correct answer is tan inverse x?.
Integrate 1/(x^2+1), correct answer is tan inverse x? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Integrate 1/(x^2+1), correct answer is tan inverse x? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Integrate 1/(x^2+1), correct answer is tan inverse x?.
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