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