What is the integral of (10)/(1-sin^2(x)) ?

The integral of (10)/(1-sin^2(x)) is 10tan(x)+C

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integral of (10)/(1-sin^2(x))

\int \frac{10}{1 - sin ^{2} ( x )} d x

10 tan (x) + C

Solution steps

\int \frac{10}{1 - sin ^{2} ( x )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \int \frac{1}{1 - sin ^{2} ( x )} d x

Rewrite using trig identities

= 10 \cdot \int sec^{2} (x) d x

Use the common integral:

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

= 10 tan (x)

Add a constant to the solution

= 10 tan (x) + C

What is the integral of (10)/(1-sin^2(x)) ?
The integral of (10)/(1-sin^2(x)) is 10tan(x)+C