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

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

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integral of 2sin(x)cos(x)

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

sin^{2} (x) + C

Solution steps

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

Take the constant out:

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

= 2 \cdot \int sin (x) cos (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{\partial}{\partial x} (ln (x^{2} + 3))

x \to 2 lim (\frac{2 x - 4}{x - 2})

(3 x^{2} + y - 4) - (2 y - x) \frac{d y}{d x} = 0

\int 3 ln (x) d x

\int e^{l n (x)} d x

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