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

The integral of sin(2x)e^{cos(2)}x is e^{cos(2)}(-1/2 xcos(2x)+1/4 sin(2x))+C

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integral of sin(2x)e^{cos(2)}x

\int sin (2 x) e^{c o s (2)} x d x

e^{c o s (2)} (- \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x)) + C

Solution steps

\int sin (2 x) e^{c o s (2)} x d x

Take the constant out:

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

= e^{c o s (2)} \cdot \int sin (2 x) x d x

Apply Integration By Parts

= e^{c o s (2)} (- \frac{1}{2} x cos (2 x) - \int - \frac{1}{2} cos (2 x) d x)

\int - \frac{1}{2} cos (2 x) d x = - \frac{1}{4} sin (2 x)

= e^{c o s (2)} (- \frac{1}{2} x cos (2 x) - (- \frac{1}{4} sin (2 x)))

Simplify

= e^{c o s (2)} (- \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x))

Add a constant to the solution

= e^{c o s (2)} (- \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x)) + C

What is the integral of sin(2x)e^{cos(2)}x ?
The integral of sin(2x)e^{cos(2)}x is e^{cos(2)}(-1/2 xcos(2x)+1/4 sin(2x))+C