What is the integral of-3cos^2(x)sin(x) ?

The integral of-3cos^2(x)sin(x) is cos^3(x)+C

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integral of-3cos^2(x)sin(x)

\int - 3 cos^{2} (x) sin (x) d x

cos^{3} (x) + C

Solution steps

\int - 3 cos^{2} (x) sin (x) d x

Take the constant out:

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

= - 3 \cdot \int cos^{2} (x) sin (x) d x

Apply u-substitution

: \int - u^{2} d u

= - 3 \cdot \int - u^{2} d u

Take the constant out:

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

= - 3 (- \int u^{2} d u)

Apply the Power Rule

: \frac{u ^{3}}{3}

= - 3 (- \frac{u ^{3}}{3})

Substitute back

u = cos (x)

= - 3 (- \frac{cos ^{3} ( x )}{3})

Simplify

- 3 (- \frac{cos ^{3} ( x )}{3}) : cos^{3} (x)

= cos^{3} (x)

Add a constant to the solution

= cos^{3} (x) + C

f (x) = 3 x^{3} + 6 x^{2} + 19

(x + y)^{2} d x + (2 x y + x^{2} - 2) d y = 0

\int \frac{2}{x ^{2} + 5 x + 6} d x

x \to 0 lim (\frac{( tan ( a x ) )}{x})

\int cos (5 x) sec^{2} (5 x) d x

What is the integral of-3cos^2(x)sin(x) ?
The integral of-3cos^2(x)sin(x) is cos^3(x)+C