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Evaluate the indefinite integral.$\int e^{2 r} \sin \left(e^{2 r}\right) d r$

$-\frac{1}{2} \cos \left(e^{2 r}\right)+C$

Calculus 1 / AB

Calculus 2 / BC

Chapter 5

Integrals

Section 4

The Substitution Rule

Integration Techniques

Missouri State University

Campbell University

Oregon State University

Baylor University

Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

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Evaluate the integral.…

01:58

Evaluate the integrals.

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Evaluate the integrals usi…

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Evaluate the indefinite in…

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Find the indefinite integr…

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Use substitution to find e…

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Evaluate the integral.

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this question asked us to evaluate the given control. We know that you is each. The two are therefore we know are 1/2 d'you is each. The two are de acts because we know when we took the derivative land up with to eat the to ours, we're bringing the 1/2 over to this side by dividing both sides by two. We can pull out the 1/2 because it's a Constance. We now have 1/2 times the integral sign of you. Do you? We know the integral of sine of you is pretty straightforward. It's negative. Co sign of you some pretty the negative next to the constant last step back. Substitute in what? Us? We don't want you in our final answer we want eat. The two are

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