What is the integral of (2+x)sin(x) ?

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

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integral of (2+x)sin(x)

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

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

Solution steps

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

Apply Integration By Parts

: - cos (x) (2 + x) - \int - cos (x) d x

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

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

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

Simplify

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

Add a constant to the solution

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

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

\int (x^{2} - 5)^{3} (2 x) d x

\int 3 x x^{2} + 1 d x

\int (\frac{1}{x} - \frac{5}{16 x ^{2} + 1}) d x

\int x^{3} - x^{2} + 1 d x

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