Explained: "Determine the following indefinite integral. ∫dx1−sin2x"

Jerold

Answered question

2021-10-29

Determine the following indefinite integral.

\int \frac{d x}{1 - \sin^{2} x}

dieseisB

Skilled2021-10-30Added 85 answers

Step 1
Given integral:

\int \frac{d x}{1 - \sin^{2} x}

Step 2
Now,
Use the following identity:

1 - \sin^{2} (x) = \cos^{2} (x)

\int \frac{1}{1 - \sin^{2} (x)} d x = \int \frac{1}{\cos^{2} (x)} d x

Use the following identity:

\frac{1}{\cos (x)} = \sec (x)

= \int \sec^{2} (x) d x

Use the common integral:

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

= \tan (x)

Add a constant to the solution:

= \tan (x) + C

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