What is the integral of (3x+a)sin(x) ?

The integral of (3x+a)sin(x) is 3(-xcos(x)+sin(x))-acos(x)+C

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integral of (3x+a)sin(x)

\int (3 x + a) sin (x) d x

3 (- x cos (x) + sin (x)) - a cos (x) + C

Solution steps

\int (3 x + a) sin (x) d x

Expand

(3 x + a) sin (x) : 3 x sin (x) + a sin (x)

= \int 3 x sin (x) + a sin (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 3 x sin (x) d x + \int a sin (x) d x

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

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

= 3 (- x cos (x) + sin (x)) - a cos (x)

Add a constant to the solution

= 3 (- x cos (x) + sin (x)) - a cos (x) + C

\int \frac{5 x ^{3} - 3 x ^{2} + 7 x - 3}{( x ^{2} + 1 ) ^{2}} d x

\int x (2 x) d x

\int x_{1} d x

\int \frac{2 t}{t ^{2} + 4} d t

What is the integral of (3x+a)sin(x) ?
The integral of (3x+a)sin(x) is 3(-xcos(x)+sin(x))-acos(x)+C