Indefinite Integral $e^x/(1+x)$

MHB
Thread starter juantheron
Start date Apr 24, 2012
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Indefinite Indefinite integral Integral

In summary, an indefinite integral is the reverse process of differentiation used to find the original function when its derivative is known. It can be solved using integration techniques such as substitution, integration by parts, or partial fractions. The indefinite integral of $e^x/(1+x)$ is $\ln(1+x) + C$, where C is the constant of integration. Its purpose is to solve problems involving rates of change and accumulation of quantities, particularly in physics and engineering. Multiple solutions are possible for indefinite integrals, differing by a constant value due to the fact that adding a constant does not change its derivative.

Apr 24, 2012

juantheron

$\displaystyle \int \frac{e^x}{1+x}dx$

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Apr 24, 2012

CaptainBlack

jacks said:

$\displaystyle \int \frac{e^x}{1+x}dx$

This is non-elementary and closely related to the exponential integral.

$\displaystyle \int \frac{e^x}{1+x}dx=\frac{{\rm{Ei}}(x+1)}{e}+C$

CB

What is an indefinite integral?

An indefinite integral is the reverse process of differentiation. It is used to find the original function when its derivative is known.

How do you solve indefinite integrals?

Indefinite integrals can be solved using integration techniques such as substitution, integration by parts, or partial fractions.

What is the indefinite integral of $e^x/(1+x)$?

The indefinite integral of $e^x/(1+x)$ is $\ln(1+x) + C$, where C is the constant of integration.

What is the purpose of finding indefinite integrals?

Finding indefinite integrals is useful in many fields of science, especially in physics and engineering, where it can be used to solve problems involving rates of change and accumulation of quantities.

Can indefinite integrals have multiple solutions?

Yes, indefinite integrals can have multiple solutions that differ by a constant value. This is because the derivative of a constant is always 0, so adding a constant to the solution does not change its derivative.