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

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

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integral of (tan(x))/(tan^2(x)+1)

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

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

Solution steps

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

Rewrite using trig identities

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

Express with sin, cos

= \int cos (x) sin (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 = sin (x)

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

Add a constant to the solution

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

\int \frac{8}{x ^{2} x ^{2} + 36} d x

\frac{d}{d t} (\frac{1}{2 t})

ln (x^{10})

y = 3 x (x + 2)^{3}

\frac{\partial}{\partial x} (- 3 x^{2} + 3)

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