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

The integral of (sin(x)cos^5(x)) is -(cos^6(x))/6+C

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integral of (sin(x)cos^5(x))

\int (sin (x) cos^{5} (x)) d x

- \frac{cos ^{6} ( x )}{6} + C

Solution steps

\int sin (x) cos^{5} (x) d x

Apply u-substitution

: \int - u^{5} d u

= \int - u^{5} d u

Take the constant out:

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

= - \int u^{5} d u

Apply the Power Rule

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

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

Substitute back

u = cos (x)

= - \frac{cos ^{6} ( x )}{6}

Add a constant to the solution

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

(4 cos (t))^{^{'}}

y = 4 x^{2}, y = 6 x^{2}, y = 6 - 5 x

x \to 3 lim (3 x - 6)

y = (x^{x} + 1)^{2}

\frac{d}{d θ} (- \frac{n}{2} \cdot ln (2 π) - \frac{n}{2} \cdot ln (θ^{2}))

What is the integral of (sin(x)cos^5(x)) ?
The integral of (sin(x)cos^5(x)) is -(cos^6(x))/6+C