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

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

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

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

\frac{tan ^{2} ( x )}{2} + C

Solution steps

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

Rewrite using trig identities

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = tan (x)

= \frac{tan ^{2} ( x )}{2}

Add a constant to the solution

= \frac{tan ^{2} ( x )}{2} + C

f (x) = lo g_{e} (10 x)

\frac{d y}{d x} = sin^{2} (y)

\frac{d}{d x} (arcsec (\frac{1}{2 x ^{2} - 1}))

\int \frac{x ^{2} + 1}{x ^{3} - 6 x ^{2} + 12 x - 8} d x

\int \frac{u ^{3}}{u + 1} d u

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