What is the integral of (x-5)cos(x) ?

The integral of (x-5)cos(x) is sin(x)(x-5)+cos(x)+C

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integral of (x-5)cos(x)

\int (x - 5) cos (x) d x

sin (x) (x - 5) + cos (x) + C

Solution steps

\int (x - 5) cos (x) d x

Apply Integration By Parts

: sin (x) (x - 5) - \int sin (x) d x

= sin (x) (x - 5) - \int sin (x) d x

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

= sin (x) (x - 5) - (- cos (x))

Simplify

= sin (x) (x - 5) + cos (x)

Add a constant to the solution

= sin (x) (x - 5) + cos (x) + C

x \to 2 lim (\frac{( x - 2 )}{x - 2})

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sin (x^{4})

\int_{0}^{7} \frac{3 t}{( t - 8 ) ^{2}} d t

What is the integral of (x-5)cos(x) ?
The integral of (x-5)cos(x) is sin(x)(x-5)+cos(x)+C