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# Evaluate the integral.$\displaystyle \int \sin 8x \cos 5x dx$

## $$\int \sin 8 x \cos 5 x d x=-\frac{1}{6} \cos (3 x)-\frac{1}{26} \cos (13 x)+c$$

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Integration Techniques

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### Video Transcript

This problem is from Chapter seven section to problem number forty one in the book Calculus Early Transcendental Zane Condition by James Door and we have on indefinite inaugural of Sign of a Dicks Times Co signed by VIX and R inte Grant is of this form signed eight times co sign be in our keys. Our value may is in X in Our value of B is five. Six so we can rewrite the integral using this formula up here. So doing so, we have one half in a rule sign of a minus B. So we have eight x minus five bricks plus sign of a plus thie, which is in X plus five mics. So let's go ahead and simplify this the sign of three X and sign of thirteen x. So, in my help here to use use up if you'd like, you can go ahead and take you too. Be free X in here. We could take you to be thirteen x So evaluating these inner rules, we should obtain negative co signed three x over three minus co signed thirteen x over thirteen and plus our constant of integration and the next thing we could do is just simplify this a little bit. Clean this up. We have a negative co signed three X over six, minus code sign thirteen x over twenty six, plus he and that's our answer.

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Integration Techniques

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