What is the integral of (2x+a)cos(x) ?

The integral of (2x+a)cos(x) is 2(xsin(x)+cos(x))+asin(x)+C

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integral of (2x+a)cos(x)

\int (2 x + a) cos (x) d x

2 (x sin (x) + cos (x)) + a sin (x) + C

Solution steps

\int (2 x + a) cos (x) d x

Expand

(2 x + a) cos (x) : 2 x cos (x) + a cos (x)

= \int 2 x cos (x) + a 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 2 x cos (x) d x + \int a cos (x) d x

\int 2 x cos (x) d x = 2 (x sin (x) + cos (x))

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

= 2 (x sin (x) + cos (x)) + a sin (x)

Add a constant to the solution

= 2 (x sin (x) + cos (x)) + a sin (x) + C

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\int \frac{100}{x ^{3}} d x

What is the integral of (2x+a)cos(x) ?
The integral of (2x+a)cos(x) is 2(xsin(x)+cos(x))+asin(x)+C