What is the integral of 5cos^2(x)sin(2x) ?

The integral of 5cos^2(x)sin(2x) is -5/2 cos^4(x)+C

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integral of 5cos^2(x)sin(2x)

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

- \frac{5}{2} cos^{4} (x) + C

Solution steps

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

Take the constant out:

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

= 5 \cdot \int cos^{2} (x) sin (2 x) d x

Apply u-substitution

: \int - u d u

= 5 \cdot \int - u d u

Take the constant out:

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

= 5 (- \int u d u)

Apply the Power Rule

: \frac{u ^{2}}{2}

= 5 (- \frac{u ^{2}}{2})

Substitute back

u = cos^{2} (x)

= 5 (- \frac{( cos ^{2} ( x ) ) ^{2}}{2})

Simplify

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

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

Add a constant to the solution

= - \frac{5}{2} cos^{4} (x) + C

\frac{d}{d x} (sin (9))

x \to 0 lim (e^{x s i n (\frac{1}{x})})

y = 3

\int \frac{1}{1 - y ^{2}} d y

f (x) = x^{4 x}

What is the integral of 5cos^2(x)sin(2x) ?
The integral of 5cos^2(x)sin(2x) is -5/2 cos^4(x)+C