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Discover the product rule, a fundamental technique for finding the derivative of a function expressed as a product of two functions. We'll learn how to apply this rule to simplify …

There's no general rule for integrating products or quotients of functions. Integration by parts may help in some special cases, but if you make up an arbitrary function, there's a good chance it …

So this expression right here is the product of the Laplace transform of 2 sine of t, and the Laplace transform of cosine of t. Now, our convolution theorem told us this right here. That if we want …

Review your knowledge of the Product rule for derivatives, and use it to solve problems.

The indefinite integral of tangent of x is, and it's neat they're connected in this way, is the negative natural log of the absolute value of cosine of x plus c.

The integral of u prime times v. That equals uv. So that's minus 1 over s e to the minus st, times v, sine of at, minus the integral. And when you do the integration by parts, this could be an …

In differential calculus we learned that the derivative of ln(x) is 1/x. Integration goes the other way: the integral (or antiderivative) of 1/x should be a function whose derivative is 1/x. As we just …

Examples of calculating definite integrals of polynomials using the fundamental theorem of calculus and the reverse power rule.

There are three parts to the integral: 1) the function part, x^2, represents the length of the rectangles--you can also think of it as the height of the function, or the y-value; 2) the dx in the …