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

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

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

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

sin^{2} (t) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

= 2 \cdot \int u d u

Apply the Power Rule

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

Substitute back

u = sin (t)

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

Simplify

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

= sin^{2} (t)

Add a constant to the solution

= sin^{2} (t) + C

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