What is the integral of sin^4(x)*cos(x) ?

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

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integral of sin^4(x)*cos(x)

\int sin^{4} (x) \cdot cos (x) d x

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

Solution steps

\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

x, x, [0, 2]

f (x) = x^{2} - 6 x + 25, at x = 0

f (x) = x^{4} + 7 e^{x}, (0, 7)

\int \frac{9 sin ^{3} ( x )}{cos ( x )} d x

x \to 5 lim (5 x - 4)

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