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Integrate the function $\frac{1}{e^{2x}}$ from $1$ to $\infty $

Step-by-step Solution

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Solution

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Final answer to the problem

The integral diverges.

Step-by-step Solution

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Rewrite the fraction $\frac{1}{e^{2x}}$ inside the integral as the product of two functions: $1\left(\frac{1}{e^{2x}}\right)$

$\int1\left(\frac{1}{e^{2x}}\right)dx$

Learn how to solve quadratic equations problems step by step online.

$\int1\left(\frac{1}{e^{2x}}\right)dx$

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Learn how to solve quadratic equations problems step by step online. Integrate the function 1/(e^(2x)) from 1 to infinity. Rewrite the fraction \frac{1}{e^{2x}} inside the integral as the product of two functions: 1\left(\frac{1}{e^{2x}}\right). We can solve the integral \int1\left(\frac{1}{e^{2x}}\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v.

Final answer to the problem

The integral diverges.

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of (1/(e^2x))dx from 1 to infinity using partial fractionsSolve integral of (1/(e^2x))dx from 1 to infinity using basic integralsSolve integral of (1/(e^2x))dx from 1 to infinity using u-substitutionSolve integral of (1/(e^2x))dx from 1 to infinity using tabular integrationSolve integral of (1/(e^2x))dx from 1 to infinity using trigonometric substitution

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Function Plot

Plotting: $\frac{1}{e^{2x}}$

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Main Topic: Quadratic Equations

The quadratic equations (or second degree equations) are those equations where the greatest exponent to which the unknown is raised is the exponent 2.

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