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

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

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

\int tan (x) l e f t (sec (x))^{2} d x

\frac{e l f t}{2} tan^{2} (x) + C

Solution steps

\int tan (x) l e f t (sec (x))^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= l f t e \cdot \int (sec (x))^{2} tan (x) d x

Apply u-substitution

: \int u d u

= l f t e \cdot \int u d u

Apply the Power Rule

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

= l f t e \frac{u ^{2}}{2}

Substitute back

u = tan (x)

= l f t e \frac{tan ^{2} ( x )}{2}

Simplify

l f t e \frac{tan ^{2} ( x )}{2} : \frac{e l f t}{2} tan^{2} (x)

= \frac{e l f t}{2} tan^{2} (x)

Add a constant to the solution

= \frac{e l f t}{2} tan^{2} (x) + C

\int t^{2} sinh (t) d t

\int_{0}^{1} \frac{x ^{2}}{x ^{3} + 1} d x

x \to 0.01 lim (\frac{e ^{x} - 1}{x})

\frac{d}{d x} (\frac{sin ( \frac{1}{x} ) x ^{3}}{ln ( x )})

1 - x^{2}, x^{6} - x + 1

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