What is the integral of (t-3)cos(t-3) ?

The integral of (t-3)cos(t-3) is -tsin(-t+3)-3sin(t-3)+cos(-t+3)+C

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integral of (t-3)cos(t-3)

\int (t - 3) cos (t - 3) d t

- t sin (- t + 3) - 3 sin (t - 3) + cos (- t + 3) + C

Solution steps

\int (t - 3) cos (t - 3) d t

Apply Integration By Parts

: sin (t - 3) (t - 3) - \int sin (t - 3) d t

= sin (t - 3) (t - 3) - \int sin (t - 3) d t

\int sin (t - 3) d t = t sin (t - 3) + t sin (3 - t) - cos (3 - t)

= sin (t - 3) (t - 3) - (t sin (t - 3) + t sin (3 - t) - cos (3 - t))

Simplify

sin (t - 3) (t - 3) - (t sin (t - 3) + t sin (3 - t) - cos (3 - t)) : - t sin (- t + 3) - 3 sin (t - 3) + cos (- t + 3)

= - t sin (- t + 3) - 3 sin (t - 3) + cos (- t + 3)

Add a constant to the solution

= - t sin (- t + 3) - 3 sin (t - 3) + cos (- t + 3) + C

\frac{\partial}{\partial x} (x e^{x y})

\int_{- 6}^{6} \frac{1}{36 - x ^{2}} d x

\int \frac{1}{( 3 x + 1 )} d x

x \to 3 + lim (\frac{x + 4}{x - 3})

f (x) = cot^{2} (cos (θ))

What is the integral of (t-3)cos(t-3) ?
The integral of (t-3)cos(t-3) is -tsin(-t+3)-3sin(t-3)+cos(-t+3)+C