What is the integral of xsin(x)+cos(x)+c ?

The integral of xsin(x)+cos(x)+c is -xcos(x)+2sin(x)+cx+C

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integral of xsin(x)+cos(x)+c

\int x sin (x) + cos (x) + c d x

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

Solution steps

\int x sin (x) + cos (x) + c 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 x sin (x) d x + \int cos (x) d x + \int c d x

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

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

\int c d x = c x

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (- 3 cos (x) + x sin (x))

y^{^{'}} (y^{3} - x) = y

\int \frac{1}{x + 9} d x

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

y^{^{''}} + 8 y^{^{'}} + 41 y = 0, y (0) = 2, y^{^{'}} (0) = - 7

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