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

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

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integral of (2sin(x)+x)

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

- 2 cos (x) + \frac{x ^{2}}{2} + C

Solution steps

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

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

\int x d x = \frac{x ^{2}}{2}

= - 2 cos (x) + \frac{x ^{2}}{2}

Add a constant to the solution

= - 2 cos (x) + \frac{x ^{2}}{2} + C

\int \frac{1}{( 7 - 8 x )} d x

n = 1 \sum \infty 99

k = 1 \sum \infty (- \frac{3}{4})^{k - 1}

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

\int cos^{8} (4 - x) sin (4 - x) d x

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