# Antiderivative of ((tanx)^2)((secx)^3)dx

• alingy1
In summary, the conversation revolved around a teacher's instruction to turn all tan and sec into cos and sin. The person asking for help did not understand how to solve this and asked for a hint. They clarified that they knew what the teacher meant by the instruction, but were unsure of the next step.
alingy1
My teacher said to turn all tan and sec to cos and sin. I still do not understand how I can solve this. Can you give me a hint? I know what he means by turning to cos and sin, but what do I do next?

alingy1 said:
My teacher said to turn all tan and sec to cos and sin. I still do not understand how I can solve this. Can you give me a hint? I know what he means by turning to cos and sin, but what do I do next?

Show us what you get when you turn all tan and sec into sin and cos.

## 1. What is an antiderivative?

An antiderivative, also known as the indefinite integral, is the reverse process of differentiation. It is a function whose derivative is equal to the given function.

## 2. How do you find the antiderivative of a given function?

To find the antiderivative, you can use the power rule, product rule, quotient rule, or chain rule, depending on the form of the function. You can also use tables of standard antiderivatives or integration techniques such as integration by parts or substitution.

## 3. What is the antiderivative of ((tanx)^2)((secx)^3)dx?

The antiderivative of ((tanx)^2)((secx)^3)dx is ((secx)^5)/5 + C.

## 4. How do you integrate trigonometric functions?

To integrate trigonometric functions, you can use trigonometric identities, substitution, or integration by parts. It is important to be familiar with trigonometric identities and their derivatives in order to solve these types of integrals.

## 5. Can you explain the steps to find the antiderivative of ((tanx)^2)((secx)^3)dx?

First, use the power rule to bring the 2 from the numerator to the denominator, resulting in (secx)^5. Then, use the power rule again to bring the 3 from the denominator to the numerator, resulting in ((secx)^5)/3. Finally, add the constant of integration, C, to the end of the antiderivative.

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