What is the integral from 0 to t of 5e^ssin(t-s) ?

The integral from 0 to t of 5e^ssin(t-s) is 5/2 e^t-5(1/2 cos(t)+1/2 sin(t))

integral from 0 to t of 5e^ssin(t-s)

\int_{0}^{t} 5 e^{s} sin (t - s) d s

\frac{5}{2} e^{t} - 5 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

Solution steps

\int_{0}^{t} 5 e^{s} sin (t - s) d s

Compute the indefinite integral:

\int 5 e^{s} sin (t - s) d s = 5 (\frac{e ^{s} cos ( - s + t )}{2} + \frac{e ^{s} sin ( - s + t )}{2}) + C

Compute the boundaries:

\int_{0}^{t} 5 e^{s} sin (t - s) d s = \frac{5}{2} e^{t} - 5 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

= \frac{5}{2} e^{t} - 5 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

\int \frac{cos ( x )}{( sin ^{2} ( x ) ) ^{\frac{1}{3}}} d x

x \to 0 lim (\frac{sin ( 14 x )}{x})

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

f (x) = 8 (2 x - 3)^{3}

(- 3, 7), (6, - 8)

What is the integral from 0 to t of 5e^ssin(t-s) ?
The integral from 0 to t of 5e^ssin(t-s) is 5/2 e^t-5(1/2 cos(t)+1/2 sin(t))