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

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

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

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

\frac{sec ^{4} ( x )}{4} + C

Solution steps

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

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = sec (x)

= \frac{sec ^{4} ( x )}{4}

Add a constant to the solution

= \frac{sec ^{4} ( x )}{4} + C

\frac{d}{d x} (- \frac{13 e ^{\frac{1}{x}}}{x ^{2}})

x \to 14 lim (x^{2} - 9)

y = \frac{1}{x}, y = x

\int 4 x^{2} - x^{4} d x

x \to - 1 + lim (x + 2)

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