What is the integral of 7cos^2(x)sin(2x) ?

The integral of 7cos^2(x)sin(2x) is -7/2 cos^4(x)+C

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integral of 7cos^2(x)sin(2x)

\int 7 cos^{2} (x) sin (2 x) d x

- \frac{7}{2} cos^{4} (x) + C

Solution steps

\int 7 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

= 7 \cdot \int cos^{2} (x) sin (2 x) d x

Apply u-substitution

: \int - u d u

= 7 \cdot \int - u d u

Take the constant out:

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

= 7 (- \int u d u)

Apply the Power Rule

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

= 7 (- \frac{u ^{2}}{2})

Substitute back

u = cos^{2} (x)

= 7 (- \frac{( cos ^{2} ( x ) ) ^{2}}{2})

Simplify

7 (- \frac{( cos ^{2} ( x ) ) ^{2}}{2}) : - \frac{7}{2} cos^{4} (x)

= - \frac{7}{2} cos^{4} (x)

Add a constant to the solution

= - \frac{7}{2} cos^{4} (x) + C

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What is the integral of 7cos^2(x)sin(2x) ?
The integral of 7cos^2(x)sin(2x) is -7/2 cos^4(x)+C