What is the integral of 3e^xsin(x) ?

The integral of 3e^xsin(x) is 3(-(e^xcos(x))/2+(e^xsin(x))/2)+C

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integral of 3e^xsin(x)

\int 3 e^{x} sin (x) d x

3 (- \frac{e ^{x} cos ( x )}{2} + \frac{e ^{x} sin ( x )}{2}) + C

Solution steps

\int 3 e^{x} sin (x) d x

Take the constant out:

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

= 3 \cdot \int e^{x} sin (x) d x

Apply Integration By Parts

: - e^{x} cos (x) - \int - e^{x} cos (x) d x

= 3 (- e^{x} cos (x) - \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

= 3 (- e^{x} cos (x) - (- \int e^{x} cos (x) d x))

Apply Integration By Parts

: e^{x} sin (x) - \int e^{x} sin (x) d x

= 3 (- e^{x} cos (x) - (- (e^{x} sin (x) - \int e^{x} sin (x) d x)))

Therefore

3 \cdot \int e^{x} sin (x) d x = 3 (- e^{x} cos (x) - (- (e^{x} sin (x) - \int e^{x} sin (x) d x)))

Isolate

\int e^{x} sin (x) d x

= 3 (- \frac{e ^{x} cos ( x )}{2} + \frac{e ^{x} sin ( x )}{2})

Add a constant to the solution

= 3 (- \frac{e ^{x} cos ( x )}{2} + \frac{e ^{x} sin ( x )}{2}) + C

4 (t) + ∣ 4 (t) - 1 ∣

\int \frac{1}{( x ^{2} - 6 x + 13 ) ^{2}} d x

\int_{0}^{1} \frac{50}{4 y - 1} d y

{t + e^{2 t}}

x \cdot (y^{2} - 1) = y \cdot (4 - x^{2}) \cdot y^{^{'}}

What is the integral of 3e^xsin(x) ?
The integral of 3e^xsin(x) is 3(-(e^xcos(x))/2+(e^xsin(x))/2)+C