What is the integral of exsin(x) ?

The integral of exsin(x) is e(-xcos(x)+sin(x))+C

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integral of exsin(x)

\int e x sin (x) d x

e (- x cos (x) + sin (x)) + C

Solution steps

\int e x sin (x) d x

Take the constant out:

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

= e \cdot \int x sin (x) d x

Apply Integration By Parts

: - x cos (x) - \int - cos (x) d x

= e (- x cos (x) - \int - cos (x) d x)

\int - cos (x) d x = - sin (x)

= e (- x cos (x) - (- sin (x)))

Simplify

= e (- x cos (x) + sin (x))

Add a constant to the solution

= e (- x cos (x) + sin (x)) + C

\frac{x}{2}

y^{^{''}} + 9 y = 2 csc^{2} (3 t)

\frac{d}{d x} (C e^{2 x})

\int \frac{x}{x ^{2} - 4 x + 8} d x

(4 + t^{2}) (\frac{d y}{d t}) + 2 t y = 4 t

What is the integral of exsin(x) ?
The integral of exsin(x) is e(-xcos(x)+sin(x))+C