Integrate Sin(3x)Cos(4x) by Tabular Method - No Trig Identities Needed | Glass of Numbers

In this video, we use the traditional method of integration by parts to find the antiderivative of a product of two different trigonometric function: sin(3x)cos(4x).

It is presented in textbooks that we are using the product-to-sum formula to turn this expression into a sum. But actually, we don't need to.

It does not matter whether we use u = sin(3x) or u = cos(4x), we are still going to get back to the original problem. So it looks like we are going in a loop!

See how to integrate this using the traditional method of integration by parts (IBP):

See another video in which we go in a loop when integrating e^(-2x)sin(3x):

See how to integrate this without using integration by parts:

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#Calculus #Integration #Integral

[Ni]

I really like your use of colors with the tabular method. It's clean and it shows the flow to the solution without unnecessary or confusing chatter and arm waving. Very nicely done!

[spiderhead]

where did 7/16 come from? isn't it supposed to be 9/16 ?