What is the integral of tan(x)*sec^2(x) ?

The integral of tan(x)*sec^2(x) is (tan^2(x))/2+C

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integral of tan(x)*sec^2(x)

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

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

Solution steps

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

Apply u-substitution

= \int u d u

Apply the Power Rule

= \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

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

\frac{d}{d x} (x^{6} ln (x))

\frac{d}{d x} (- 2 cos (x) sin (x) - 2 cos (x))

x \to π lim (\frac{tan ( x )}{sin ( 2 x )})

9 e^{- x}

What is the integral of tan(x)*sec^2(x) ?
The integral of tan(x)*sec^2(x) is (tan^2(x))/2+C