What is the integral of sin(x)cos^6(x) ?

The integral of sin(x)cos^6(x) is -(cos^7(x))/7+C

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integral of sin(x)cos^6(x)

\int sin (x) cos^{6} (x) d x

- \frac{cos ^{7} ( x )}{7} + C

Solution steps

\int sin (x) cos^{6} (x) d x

Apply u-substitution

: \int - u^{6} d u

= \int - u^{6} d u

Take the constant out:

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

= - \int u^{6} d u

Apply the Power Rule

: \frac{u ^{7}}{7}

= - \frac{u ^{7}}{7}

Substitute back

u = cos (x)

= - \frac{cos ^{7} ( x )}{7}

Add a constant to the solution

= - \frac{cos ^{7} ( x )}{7} + C

x \to 0 lim (cos^{2} (x))

\frac{x ^{2} + 1}{x - 2}

\frac{d}{d x} ((x^{4} - 2)^{5})

8 x^{\frac{3}{2}}

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

What is the integral of sin(x)cos^6(x) ?
The integral of sin(x)cos^6(x) is -(cos^7(x))/7+C