# Trig Integral Question: Which Method is Correct?

• physstudent1
In summary: I take that back. I tried it and it didn't work, lol. But your solution is still right, but the limits of Integration is a different story.
physstudent1

## Homework Statement

Evaluate the integral

integral of (tanx)^5*(secx)^4

## The Attempt at a Solution

what I did was broke the sec^4x into 2 sec^2's multiplied by each other
then one of these terms became tan^2x +1
so I had tan^5x*(tan^2x + 1)*sec^2x

then u = tanx
du = sec^2x

eventual answer tan^8x/8 + tan^6x/6 + c

however the book shows this problem by taking a (secxtanx) out of eveyrthing then doing tan^4x = (sec^2x -1)^2*sec^3x
u= secx
du = tanxsecx

eventual answer sec^8x/8 - sec^6x/3 + sec^4x/4 + C

...is there something wrong with the way I did it; I don't see anything wrong with the way I'm doing it but the book insists on doing all problems like this the otherway. I wouldn't mind but I don't like memorizing things and the way I always seem to think of doing these problems is the first method I wrote out please respond I have an exam on this stuff tomarrow night

$$\int\sec^{4}x\tan^{5}xdx$$

$$\int\sec^{3}x\tan^{4}x(\sec x\tan x)dx$$

$$\int\sec^{3}x(\sec^{2}x-1)^2(\sec x\tan x)dx$$

yes that is how the book does it but why is the way that I did it wrong I don't get it?

$$\int\sec^{4}x\tan^{5}xdx$$

$$\int(\tan^{2}x+1)\tan^{5}x\sec^{2}xdx$$

I guess just have confidence in yourself. You did it all the steps correctly, but through a different route.

Last edited:
ok thanks alot; and wow that's a good way to proove it I didn't think of that

physstudent1 said:
ok thanks alot; and wow that's a good way to proove it I didn't think of that
I take that back. I tried it and it didn't work, lol. But your solution is still right, but the limits of Integration is a different story.

ah yea that does make sense that you would need different limits

## 1. What is a trigonometric integral?

A trigonometric integral is an integral that involves trigonometric functions such as sine, cosine, and tangent. It is used to find the area under a curve that is defined by a trigonometric function.

## 2. How do I solve a trigonometric integral?

Solving a trigonometric integral involves using integration techniques such as substitution, integration by parts, or trigonometric identities. It is important to understand the properties and rules of trigonometric functions in order to successfully solve a trigonometric integral.

## 3. What is the purpose of solving a trigonometric integral?

The purpose of solving a trigonometric integral is to find the exact value of the area under a curve that is defined by a trigonometric function. This can be useful in many applications, such as in physics, engineering, and mathematics.

## 4. Can I use a calculator to solve a trigonometric integral?

While some calculators have the capability to solve simple trigonometric integrals, it is important to understand the concepts and techniques behind solving them by hand. Additionally, more complex trigonometric integrals may require integration by parts or other techniques that cannot be done on a calculator.

## 5. Are there any common mistakes to avoid when solving a trigonometric integral?

Some common mistakes to avoid when solving a trigonometric integral include incorrect use of trigonometric identities, forgetting to include the constant of integration, and making errors in algebraic manipulation. It is important to double check your work and be familiar with the properties and rules of trigonometric functions to avoid these mistakes.

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