What is the integral of (3x+1)cos(x) ?

The integral of (3x+1)cos(x) is sin(x)(3x+1)+3cos(x)+C

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integral of (3x+1)cos(x)

\int (3 x + 1) cos (x) d x

sin (x) (3 x + 1) + 3 cos (x) + C

Solution steps

\int (3 x + 1) cos (x) d x

Apply Integration By Parts

: (3 x + 1) sin (x) - \int 3 sin (x) d x

= (3 x + 1) sin (x) - \int 3 sin (x) d x

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

= (3 x + 1) sin (x) - (- 3 cos (x))

Simplify

= sin (x) (3 x + 1) + 3 cos (x)

Add a constant to the solution

= sin (x) (3 x + 1) + 3 cos (x) + C

\int e^{- 13 x} d x

\frac{18}{s ^{2} + 5 s + 6} + \frac{6}{s}

(4 x + 3) (x^{2} - 1)^{2}

\frac{d}{d x} ((\frac{x}{x ^{2} + 1})^{2})

x \to e lim (\frac{1}{2} ln (x))

What is the integral of (3x+1)cos(x) ?
The integral of (3x+1)cos(x) is sin(x)(3x+1)+3cos(x)+C