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Integrate 1/(x^2+1 )?
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Integrate 1/(x^2+1 )?
Integration of 1/(x^2+1)
To integrate 1/(x^2+1), we can use the substitution method. Let u = x^2+1, then du/dx = 2x and dx = du/2x.
Substituting u and dx in the integral, we get:
∫1/(x^2+1) dx = ∫1/u * (du/2x) = (1/2) ∫1/u du
Now, integrating 1/u with respect to u, we get:
(1/2) ln|u| + C
Substituting back the value of u, we get:
(1/2) ln|x^2+1| + C
Therefore, the final answer to the integral of 1/(x^2+1) is:
∫1/(x^2+1) dx = (1/2) ln|x^2+1| + C
To integrate 1/(x^2+1), we can use the substitution method. Let u = x^2+1, then du/dx = 2x and dx = du/2x.
Substituting u and dx in the integral, we get:
∫1/(x^2+1) dx = ∫1/u * (du/2x) = (1/2) ∫1/u du
Now, integrating 1/u with respect to u, we get:
(1/2) ln|u| + C
Substituting back the value of u, we get:
(1/2) ln|x^2+1| + C
Therefore, the final answer to the integral of 1/(x^2+1) is:
∫1/(x^2+1) dx = (1/2) ln|x^2+1| + C
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Integrate 1/(x^2+1 )?
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Integrate 1/(x^2+1 )? 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 )? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Integrate 1/(x^2+1 )?.
Integrate 1/(x^2+1 )? 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 )? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Integrate 1/(x^2+1 )?.
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