Question Video: Integrating Reciprocal Trigonometric Functions | Nagwa Question Video: Integrating Reciprocal Trigonometric Functions | Nagwa

Question Video: Integrating Reciprocal Trigonometric Functions Mathematics • Second Year of Secondary School

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Determine ∫ 6 sec² 5𝑥 d𝑥.

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Video Transcript

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

In this question, we’re 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 𝑎 and 𝑘, where 𝑎 is not equal to zero, the integral of 𝑘 times the sec squared of 𝑎𝑥 with respect to 𝑥 is equal to 𝑘 times the tan of 𝑎𝑥 all divided by 𝑎 plus the constant of integration 𝐶. And we can apply this directly to the integral given to us in the question. We’ll set our value of 𝑘 equal to six and our value of 𝑎 equal to five.

So by substituting these values into our integral result, we get six times the tan of five 𝑥 divided by five plus our constant of integration 𝐶. And we’ll rewrite this as six over five times the tan of five 𝑥 plus 𝐶.

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

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