`int (tan^2(y) + 1) dy` Find the indefinite integral.

Textbook Question

Chapter 4, 4.1 - Problem 31 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the indefinite integral and yo need to use the following trigonometric formula `1 + tan^2 y = 1/(cos^2 y).`

Replacing `1/(cos^2 y)` for `1 + tan^2 y` yields:

`int (1 + tan^2 y) dy = int (dy)/(cos^2 y)`

You need to remember that `1/(cos^2 y) = (tan y)'.`

`int (dy)/(cos^2 y) = int (tan y)' = tan y + C`

Hence, evaluating the given indefinite integral, yields` int (1 + tan^2 y) dy =tan y + C.`

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