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Determine β« 6 secΒ² 5π₯ dπ₯.

Determine the integral of six times the sec squared of five π₯ with respect to π₯.

In this question, weβre asked to evaluate the integral of a trigonometric function. And in this case, we can recall an integral result which will help us evaluate this. We know for any real constants π and π, where π is not equal to zero, the integral of π times the sec squared of ππ₯ with respect to π₯ is equal to π times the tan of ππ₯ all divided by π plus the constant of integration πΆ. And we can apply this directly to the integral given to us in the question. Weβll set our value of π equal to six and our value of π equal to five.

So by substituting these values into our integral result, we get six times the tan of five π₯ divided by five plus our constant of integration πΆ. And weβll rewrite this as six over five times the tan of five π₯ plus πΆ.

Therefore, we were able to show the integral of six times the sec squared of five π₯ with respect to π₯ is equal to six over five times the tan of five π₯ plus πΆ.

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