What is the integral of 2sin(t)cos(t)e^{-cos(t)} ?

The integral of 2sin(t)cos(t)e^{-cos(t)} is 2(e^{-cos(t)}cos(t)+e^{-cos(t)})+C

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integral of 2sin(t)cos(t)e^{-cos(t)}

\int 2 sin (t) cos (t) e^{- c o s (t)} d t

2 (e^{- c o s (t)} cos (t) + e^{- c o s (t)}) + C

Solution steps

\int 2 sin (t) cos (t) e^{- c o s (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) e^{- c o s (t)} d t

Apply Integration By Parts

: e^{- c o s (t)} cos (t) - \int - e^{- c o s (t)} sin (t) d t

= 2 (e^{- c o s (t)} cos (t) - \int - e^{- c o s (t)} sin (t) d t)

\int - e^{- c o s (t)} sin (t) d t = - e^{- c o s (t)}

= 2 (e^{- c o s (t)} cos (t) - (- e^{- c o s (t)}))

Simplify

= 2 (e^{- c o s (t)} cos (t) + e^{- c o s (t)})

Add a constant to the solution

= 2 (e^{- c o s (t)} cos (t) + e^{- c o s (t)}) + C

y = x^{4} + 3 e^{x}

tan (x + 1)

\frac{d}{d x} (ln (3 + x))

\frac{\partial}{\partial x} (e^{x yz} + x yz)

\frac{d}{d x} ((3 x + 4) x^{2})

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