What is the integral of (sin(y)+ysin(x)+1/x) ?

The integral of (sin(y)+ysin(x)+1/x) is ln|x|+sin(y)x-ycos(x)+C

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integral of (sin(y)+ysin(x)+1/x)

\int (sin (y) + y sin (x) + \frac{1}{x}) d x

ln ∣ x ∣ + sin (y) x - y cos (x) + C

Solution steps

\int sin (y) + y sin (x) + \frac{1}{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 \frac{1}{x} d x + \int sin (y) d x + \int sin (x) y d x

\int \frac{1}{x} d x = ln ∣ x ∣

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

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

= ln ∣ x ∣ + sin (y) x - y cos (x)

Add a constant to the solution

= ln ∣ x ∣ + sin (y) x - y cos (x) + C

\frac{d}{d x} (x^{2} \cdot x)

\frac{s}{( s - 3 ) ( s - 6 ) ( s - 2 )}

\int_{0}^{0.4} \frac{( x ^{2} )}{4 - 25 x ^{2}} d x

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

\frac{d}{d x} ((x^{5} - 9) x)

What is the integral of (sin(y)+ysin(x)+1/x) ?
The integral of (sin(y)+ysin(x)+1/x) is ln|x|+sin(y)x-ycos(x)+C