# Solving Integrals of Problem Homework Statement

• IncognitoSOS
In summary, the conversation is about two integration problems, one involving (1+2t^8)^20 * t^7 dt and the other involving dx/(x*ln(X^5)). The person is seeking help and the conversation suggests trying u-substitution for the first problem and simplifying ln(x^5) for the second problem. However, there is a potential issue with the second problem as x cannot equal 1 or 0.
IncognitoSOS

## Homework Statement

I have two problems that I am stuck on, any help would be appreciated
1. the Integral of (1+2t^8)^20 * t^7 dt
2. the Integral from 0 to 1 of dx/(x*ln(X^5))

## The Attempt at a Solution

for 1. I know that to something like this with a lower power you should multiply it out and then use the power rule, but am I stuck multiplying out 1+2t^8 twenty times?
for 2. Calculator gave me various errors. I suspect that the answer is zero, but I'm not sure.

Thanks to anyone who decides to post

For number 1, have you tried u-substitution? Whenever you have an integral that you can't immediately figure out how to integrate, you should always try u-substitution.

For part 2, you can simplify ln(x^5) into 5lnx. Can you find the indefinite integral from here?

for question 2,
You've got a problem with this question which u will find out once u find the indefinite integral. x can't equal to either 1 or 0.

## 1. What is an integral?

An integral is a mathematical concept used to calculate the area under a curve in a graph. It is also known as the anti-derivative of a function.

## 2. Why is it important to solve integrals?

Solving integrals allows us to find the exact value of an area under a curve, which is useful in many real-world applications such as physics, engineering, and economics.

## 3. What are the different methods for solving integrals?

There are several methods for solving integrals, including substitution, integration by parts, partial fractions, and trigonometric substitution.

## 4. How do I know which method to use?

The method you should use to solve an integral depends on the complexity of the function and the techniques you have learned. It is helpful to practice and gain experience with different methods to determine which one is most suitable for a given problem.

## 5. What are some tips for solving integrals efficiently?

Some tips for solving integrals efficiently include identifying patterns, using appropriate substitutions, and simplifying the integrand before attempting to integrate. It is also important to practice and familiarize yourself with common integrals and their solutions.

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