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teng125
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integ [e^x / (1 + e^2x ) ]dx.can someone show me how to solve this by using 1 / (1 + x^2 ) formula??
pls...
pls...
Integrating [e^x / (1 + e^2x ) ]dx
- Thread starter teng125
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In summary, the conversation discusses how to solve the integral of [e^x / (1 + e^2x)]dx using the formula 1 / (1 + x^2). The individual asks for guidance and suggests arranging the equation to [e^x / (1 + {e^x}^2)], but is unable to relate it to the formula. Another person suggests using a clever change of variables to eliminate the e^x in the numerator. The conversation ends with the individual correctly identifying the substitution of e^x by u and differentiating to find the solution.
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arildno
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What have you done?
- #3
teng125
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i think of arranging it to be [e^x / (1 + {e^x}^2 ) ] but cannot related it to 1 / 1 + x^2
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arildno
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Good move! 
Now, is it a clever change of variables that leaps into your eyes?
Now, is it a clever change of variables that leaps into your eyes?
- #5
teng125
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for the differentiation arctan x result is 1 / 1 + x^2 but for this ques how about the e^x on the numerator??
- #6
assyrian_77
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HINT: You can "get rid" of the [tex]e^x[/tex] in the numerator by a simple change of variables.
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teng125
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is it just subs e^x by u then diff du = e^x dx ??
- #8
assyrian_77
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Yes, that is correct.
FAQ: Integrating [e^x / (1 + e^2x ) ]dx
What is the formula for integrating [e^x / (1 + e^2x)]dx?
The formula for integrating [e^x / (1 + e^2x)]dx is ∫e^x / (1 + e^2x) dx = 1/2 ln(1 + e^2x) + C.
How do you solve the integral of [e^x / (1 + e^2x)]dx?
To solve the integral of [e^x / (1 + e^2x)]dx, first use the substitution u = 1 + e^2x. This will change the integral to ∫e^x / u du. Then, use the formula for integrating ln(u) to get the final answer of 1/2 ln(1 + e^2x) + C.
Can [e^x / (1 + e^2x)]dx be solved without using a substitution?
No, the integral of [e^x / (1 + e^2x)]dx cannot be solved without using a substitution. The substitution u = 1 + e^2x is necessary in order to simplify the integral and make it solvable.
What is the significance of the constant C in the solution to the integral of [e^x / (1 + e^2x)]dx?
The constant C in the solution to the integral of [e^x / (1 + e^2x)]dx represents the arbitrary constant that is added when taking the indefinite integral. This is because the derivative of a constant is 0, so any constant value added to the integral will not affect the final answer.
What are some applications of integrating [e^x / (1 + e^2x)]dx?
The integral of [e^x / (1 + e^2x)]dx has many applications in the fields of physics, engineering, and economics. It can be used to model growth and decay processes, such as the population growth of a species or the decay of a radioactive substance. It can also be used in circuit analysis and in determining the area under a curve in economic models.