What is the integral of excos(x) ?

The integral of excos(x) is e(xsin(x)+cos(x))+C

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integral of excos(x)

\int e x cos (x) d x

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

cos^{9} (t)

\frac{\partial}{\partial x} (2 (y^{2} - x^{2}) ln (x + y))

3 x^{2} - x^{3}

\int \frac{1}{4 x ^{2} + 1} d x

\int \frac{1}{y + y} d y

What is the integral of excos(x) ?
The integral of excos(x) is e(xsin(x)+cos(x))+C