What is the integral of (6x-1)cos(x) ?

The integral of (6x-1)cos(x) is 6(xsin(x)+cos(x))-sin(x)+C

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integral of (6x-1)cos(x)

\int (6 x - 1) cos (x) d x

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

Solution steps

\int (6 x - 1) cos (x) d x

Expand

(6 x - 1) cos (x) : 6 x cos (x) - cos (x)

= \int 6 x cos (x) - cos (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 6 x cos (x) d x - \int cos (x) d x

\int 6 x cos (x) d x = 6 (x sin (x) + cos (x))

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

= 6 (x sin (x) + cos (x)) - sin (x)

Add a constant to the solution

= 6 (x sin (x) + cos (x)) - sin (x) + C

\frac{d}{d x} (x^{l n (2)})

f (x) = 5 x + 11, at x = 5

\frac{d}{d x} (- 7 x^{2})

\frac{5 s + 12}{s + 3}

\int (2 x + 2)^{3} d x

What is the integral of (6x-1)cos(x) ?
The integral of (6x-1)cos(x) is 6(xsin(x)+cos(x))-sin(x)+C