Help me find the anitderivative of this

Thread starter moela
Start date May 27, 2008

In summary, an antiderivative is the opposite of a derivative and allows us to solve for the original function. It is useful in various applications such as physics, economics, and engineering. The process of finding an antiderivative involves using techniques such as integration by substitution, integration by parts, and partial fractions. Not every function has an antiderivative, as some require more advanced techniques to solve.

May 27, 2008

moela

What is the antiderivative of tanx/sec^99x?

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May 28, 2008

Vid

tan(x) = sin(x)/cos(x)
1/sec(x) = cos(x)

tan(x)/sec^99(x) =...?

A simple u-sub should pop right out once you simplify this.

May 28, 2008

benorin

Homework Helper

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Make the substitution [tex]u=\sec x[/tex]

What is an antiderivative?

An antiderivative is the opposite of a derivative. It is a function that, when differentiated, gives the original function.

Why do we need to find the antiderivative?

Finding the antiderivative allows us to solve for the original function, which may be useful in various applications such as physics, economics, and engineering.

How do you find the antiderivative of a function?

The process of finding an antiderivative involves using techniques such as integration by substitution, integration by parts, and partial fractions. It also requires knowledge of basic integration rules and formulas.

What are some common antiderivatives?

Some common antiderivatives include the antiderivative of x^n (x^(n+1))/(n+1), the antiderivative of sin(x) -cos(x), and the antiderivative of e^x is e^x.

Can every function have an antiderivative?

No, not every function has an antiderivative. Some functions, such as e^(x^2) and 1/(xlnx), do not have an elementary antiderivative and require more advanced techniques to solve.