What is the integral of (tan(x))/(cos^2(x)) ?

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

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integral of (tan(x))/(cos^2(x))

\int \frac{tan ( x )}{cos ^{2} ( x )} d x

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

Solution steps

\int \frac{tan ( x )}{cos ^{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

8 t \frac{d y}{d t} + y = t^{4}

\frac{\partial}{\partial y} (x + x^{2} + y^{2})

\frac{d}{d x} (\frac{6 x - 1}{4 x + 3})

\frac{\partial}{\partial v} (u v^{2})

\frac{d}{d x} (\frac{1}{( x + 8 ) ^{2}})

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