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 \infty lim (e^{\frac{- x}{100}})

x \to - 2 lim (\frac{x + 3}{x + 2})

(2 x^{2} + 2)^{3} (x^{2} - 1)^{2}

x \to 1 - lim (\frac{1}{x ^{3} - 1})

\frac{e ^{- 10 s}}{s ^{2}}

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