What is the integral of (sec^2(x)tan^4(x)) ?

The integral of (sec^2(x)tan^4(x)) is (tan^5(x))/5+C

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integral of (sec^2(x)tan^4(x))

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

\frac{tan ^{5} ( x )}{5} + C

Solution steps

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

Rewrite using trig identities

= \int (1 + tan^{2} (x)) tan^{4} (x) d x

Apply u-substitution

: \int u^{4} d u

= \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= \frac{u ^{5}}{5}

Substitute back

u = tan (x)

= \frac{tan ^{5} ( x )}{5}

Add a constant to the solution

= \frac{tan ^{5} ( x )}{5} + C

x \to 5 lim (5 x (5 - x))

\frac{d}{d x} (\frac{sin ( 10 x )}{cos ( 10 x )})

y^{^{'}} - y = 2 t e^{2} t

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

\frac{\partial}{\partial y} (x e^{5 y})

What is the integral of (sec^2(x)tan^4(x)) ?
The integral of (sec^2(x)tan^4(x)) is (tan^5(x))/5+C