What is the integral of tan(x)sec^6(x) ?

The integral of tan(x)sec^6(x) is (sec^6(x))/6+C

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integral of tan(x)sec^6(x)

\int tan (x) sec^{6} (x) d x

\frac{sec ^{6} ( x )}{6} + C

Solution steps

\int tan (x) sec^{6} (x) d x

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{u ^{6}}{6}

Substitute back

u = sec (x)

= \frac{sec ^{6} ( x )}{6}

Add a constant to the solution

= \frac{sec ^{6} ( x )}{6} + C

\frac{d}{d x} ((4 x + e^{- z^{2}})^{3})

\frac{d}{d x} (e^{\frac{x ^{2}}{2}})

\int x x - 21 d x

f (x) = \frac{7 x - 4}{- 3 x + 3}

What is the integral of tan(x)sec^6(x) ?
The integral of tan(x)sec^6(x) is (sec^6(x))/6+C