What is the integral of (3x+2)cos(x) ?

The integral of (3x+2)cos(x) is sin(x)(3x+2)+3cos(x)+C

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integral of (3x+2)cos(x)

\int (3 x + 2) cos (x) d x

sin (x) (3 x + 2) + 3 cos (x) + C

Solution steps

\int (3 x + 2) cos (x) d x

Apply Integration By Parts

: (3 x + 2) sin (x) - \int 3 sin (x) d x

= (3 x + 2) sin (x) - \int 3 sin (x) d x

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

= (3 x + 2) sin (x) - (- 3 cos (x))

Simplify

= sin (x) (3 x + 2) + 3 cos (x)

Add a constant to the solution

= sin (x) (3 x + 2) + 3 cos (x) + C

\int \frac{1}{x 4 - x ^{6}} d x

x^{2} - 1

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

\int \frac{1}{5 x - 2} - \frac{1}{5 x + 2} d x

\int (1 - x) sin (x) d x

What is the integral of (3x+2)cos(x) ?
The integral of (3x+2)cos(x) is sin(x)(3x+2)+3cos(x)+C