What is the integral of (tan^2(x))/(sec^3(x)) ?

The integral of (tan^2(x))/(sec^3(x)) is (sin^3(x))/3+C

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integral of (tan^2(x))/(sec^3(x))

\int \frac{tan ^{2} ( x )}{sec ^{3} ( x )} d x

\frac{sin ^{3} ( x )}{3} + C

Solution steps

\int \frac{tan ^{2} ( x )}{sec ^{3} ( x )} d x

Rewrite using trig identities

= \int sin^{2} (x) cos (x) d x

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = sin (x)

= \frac{sin ^{3} ( x )}{3}

Add a constant to the solution

= \frac{sin ^{3} ( x )}{3} + C

(t^{2} + 1) \frac{d y}{d t} = 2 y

\frac{\partial}{\partial x} (x^{8} + 8 x y^{7})

\int 1 d x^{3}

f (x) = \frac{x ^{2}}{ln ( x )}

\frac{d}{d x} (2 x^{2} - 6 x)

What is the integral of (tan^2(x))/(sec^3(x)) ?
The integral of (tan^2(x))/(sec^3(x)) is (sin^3(x))/3+C