Get the solution to "Find the indefinite integral. ∫(sec⁡y)(tan⁡y−sec⁡y)dy"

jeseHainsij

Answered question

2021-11-09

Find the indefinite integral.

\int (\sec y) (\tan y - \sec y) d y

Donald Proulx

Beginner2021-11-10Added 18 answers

Step 1
To evaluate the given integral

\int \sec y (\tan y - \sec y) d y

Step 2
To begin with, we remove the bracket using distributive law,

\int \sec y (\tan y - \sec y) d y = \int \sec y \tan y d y - \int \sec^{2} y d y

Now, solve the integral individually,

\int \sec y \tan y d y = \sec y + c_{1}

The second integral

\int \sec^{2} y d y = \tan y + c_{2}

Step 3
Substitute the values back to the original integral,

\int \sec y \tan y d y - \int \sec^{2} y d y = \sec y - \tan y + C

Step 4
Answer:

\int \sec y (\tan y - \sec y) d y = \sec y - \tan y + C

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