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

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

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

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

2 sin (x) + 3 cos (x) + \frac{x ^{2}}{2} + C

Solution steps

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

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

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

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

= 2 sin (x) - (- 3 cos (x)) + \frac{x ^{2}}{2}

Simplify

= 2 sin (x) + 3 cos (x) + \frac{x ^{2}}{2}

Add a constant to the solution

= 2 sin (x) + 3 cos (x) + \frac{x ^{2}}{2} + C

f (x) = (6 x + 7) (7 x - 8)

\int 10 sin (5 x) d x

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

\frac{d y}{d x} = \frac{2 x}{1 + 2 y}, y (2) = 1

\frac{2 x}{y} d x - \frac{x ^{2}}{y ^{2}} d y = 0

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