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

\int x (2 x + 1) d x

n = 1 \sum \infty \frac{1}{2 n + 4}

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

\int 2 x (x^{2} + 2)^{- 5} d x

x^{5} y^{^{'}} + y^{5} = 0

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