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

The integral of tan^4(x)cos^5(x) is (sin^5(x))/5+C

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

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

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

Solution steps

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

Rewrite using trig identities

= \int sin^{4} (x) cos (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 = sin (x)

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

Add a constant to the solution

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

f (x) = e^{x}, at x = 2

y = 4^{- x}

\frac{d}{d y} (e^{5 y})

f (x) = sin (2 x), at x = \frac{π}{4}

h \to + 0 lim (\frac{( ( x + h ) - x )}{h})

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