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

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

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integral of 2cos(x)sin(x)

\int 2 cos (x) sin (x) d x

sin^{2} (x) + C

Solution steps

\int 2 cos (x) sin (x) d x

Take the constant out:

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

= 2 \cdot \int cos (x) sin (x) d x

Apply u-substitution

: \int u d u

= 2 \cdot \int u d u

Apply the Power Rule

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

= 2 \cdot \frac{u ^{2}}{2}

Substitute back

u = sin (x)

= 2 \cdot \frac{sin ^{2} ( x )}{2}

Simplify

2 \cdot \frac{sin ^{2} ( x )}{2} : sin^{2} (x)

= sin^{2} (x)

Add a constant to the solution

= sin^{2} (x) + C

\frac{d}{d x} (14.8 sin (\frac{π}{6} \cdot x - \frac{π}{2}) + 10)

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

\frac{\partial}{\partial x} (9 x cos (x) cos (y))

\int lo g_{e} (2 x) d x

(x - 1)^{\frac{2}{3}}

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