Integrate the function $\frac{3}{x^5}$ from 0 to $1$

Step-by-step Solution

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Final answer to the problem

The integral diverges.

Step-by-step Solution

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  • Integrate by partial fractions
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Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$

$\int_{0}^{1}3x^{-5}dx$

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$\int_{0}^{1}3x^{-5}dx$

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Learn how to solve definite integrals problems step by step online. Integrate the function 3/(x^5) from 0 to 1. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as -5. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.

Final answer to the problem

The integral diverges.

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Function Plot

Plotting: $\frac{3}{x^5}$

Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

Used Formulas

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