What is the integral of tan(4x)sec^5(4x) ?

The integral of tan(4x)sec^5(4x) is 1/20 sec^5(4x)+C

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integral of tan(4x)sec^5(4x)

\int tan (4 x) sec^{5} (4 x) d x

\frac{1}{20} sec^{5} (4 x) + C

Solution steps

\int tan (4 x) sec^{5} (4 x) d x

Apply u-substitution

: \int tan (u) sec^{5} (u) \frac{1}{4} d u

= \int tan (u) sec^{5} (u) \frac{1}{4} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int tan (u) sec^{5} (u) d u

Apply u-substitution

: \int v^{4} d v

= \frac{1}{4} \cdot \int v^{4} d v

Apply the Power Rule

: \frac{v ^{5}}{5}

= \frac{1}{4} \cdot \frac{v ^{5}}{5}

Substitute back

= \frac{1}{4} \cdot \frac{sec ^{5} ( 4 x )}{5}

Simplify

\frac{1}{4} \cdot \frac{sec ^{5} ( 4 x )}{5} : \frac{1}{20} sec^{5} (4 x)

= \frac{1}{20} sec^{5} (4 x)

Add a constant to the solution

= \frac{1}{20} sec^{5} (4 x) + C

x \to 7 - lim (\frac{1}{x - 7})

x^{2} + 6

arcsin (\frac{x}{7})

y^{^{'}} = \frac{x ^{2} + 2 \cdot y ^{2}}{x \cdot y}

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

What is the integral of tan(4x)sec^5(4x) ?
The integral of tan(4x)sec^5(4x) is 1/20 sec^5(4x)+C