What is the integral of xcos(xy)+1 ?

The integral of xcos(xy)+1 is y+sin(xy)+C

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integral of xcos(xy)+1

\int x cos (x y) + 1 d y

y + sin (x y) + C

Solution steps

\int x cos (x y) + 1 d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d y + \int cos (x y) x d y

\int 1 d y = y

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

= y + sin (x y)

Add a constant to the solution

= y + sin (x y) + C

12

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

x e^{x}

f^{^{''''}} = 19 e^{x^{2}}

x \to 0 lim (\frac{1 - x}{x})