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

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##  Final answer to the problem

The integral diverges.

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
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1

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

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

Learn how to solve definite integrals problems step by step online.

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

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.

##  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

###  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