What is the integral of ln(x)+sin(pix) ?

The integral of ln(x)+sin(pix) is xln(x)-x-1/pi cos(pix)+C

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integral of ln(x)+sin(pix)

\int ln (x) + sin (π x) d x

x ln (x) - x - \frac{1}{π} cos (π x) + C

Solution steps

\int ln (x) + sin (π 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 ln (x) d x + \int sin (π x) d x

\int ln (x) d x = x ln (x) - x

\int sin (π x) d x = - \frac{1}{π} cos (π x)

= x ln (x) - x - \frac{1}{π} cos (π x)

Add a constant to the solution

= x ln (x) - x - \frac{1}{π} cos (π x) + C

\frac{2 s + 3}{( s - 7 ) ^{4}}

(3 y^{2} + 2 x) d x + (6 x y + 16 y^{3}) d y = 0

\int sin (x) - 5 cos (x) d x

y^{^{'}} - 4 y = 4 e^{6 t}

\int \frac{x}{1 - x ^{4}} d x

What is the integral of ln(x)+sin(pix) ?
The integral of ln(x)+sin(pix) is xln(x)-x-1/pi cos(pix)+C