What is the integral of ((sin(x))^2)/((cos(x))^4) ?

The integral of ((sin(x))^2)/((cos(x))^4) is (tan^3(x))/3+C

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integral of ((sin(x))^2)/((cos(x))^4)

\int \frac{( sin ( x ) ) ^{2}}{( cos ( x ) ) ^{4}} d x

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

Solution steps

\int \frac{( sin ( x ) ) ^{2}}{( cos ( x ) ) ^{4}} d x

Rewrite using trig identities

= \int sec^{4} (x) sin^{2} (x) d x

Rewrite using trig identities

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

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

Add a constant to the solution

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

\int_{1}^{4} \frac{e ^{\frac{4}{x}}}{x ^{2}} d x

\frac{d}{d x} (a e^{2 x} + b e^{x})

\frac{\partial}{\partial z} (e^{x} sin (yz))

\int 10 sin^{3} (x) cos^{7} (x) d x

\frac{\partial}{\partial x} (y^{2} - e^{x y})

What is the integral of ((sin(x))^2)/((cos(x))^4) ?
The integral of ((sin(x))^2)/((cos(x))^4) is (tan^3(x))/3+C