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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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

\int cos^{\frac{3}{2}} (x) sin^{3} (x) d x

\int e^{l n (x^{2} + 1)} d x

\int \frac{1}{y} e^{- (y + \frac{x}{y})} d x

\int - \frac{1}{x ln ( x )} d x

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