What is the integral of 18cos^2(t)sin(t) ?

The integral of 18cos^2(t)sin(t) is -6cos^3(t)+C

Popular >

integral of 18cos^2(t)sin(t)

\int 18 cos^{2} (t) sin (t) d t

- 6 cos^{3} (t) + C

Solution steps

\int 18 cos^{2} (t) sin (t) d t

Take the constant out:

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

= 18 \cdot \int cos^{2} (t) sin (t) d t

Apply u-substitution

: \int - u^{2} d u

= 18 \cdot \int - u^{2} d u

Take the constant out:

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

= 18 (- \int u^{2} d u)

Apply the Power Rule

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

= 18 (- \frac{u ^{3}}{3})

Substitute back

u = cos (t)

= 18 (- \frac{cos ^{3} ( t )}{3})

Simplify

18 (- \frac{cos ^{3} ( t )}{3}) : - 6 cos^{3} (t)

= - 6 cos^{3} (t)

Add a constant to the solution

= - 6 cos^{3} (t) + C

\frac{d}{d x} (arccsc (2 x + 1))

\frac{d}{d x} (3 - \frac{18}{5 x ^{\frac{1}{10}}})

x \to 0 lim (arctan (\frac{5}{x}))

\int 6 cos (x) d x

f (x) = 8 - x

What is the integral of 18cos^2(t)sin(t) ?
The integral of 18cos^2(t)sin(t) is -6cos^3(t)+C