What is the integral of ln(x)+sin(x)+8 ?

The integral of ln(x)+sin(x)+8 is xln(x)+7x-cos(x)+C

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integral of ln(x)+sin(x)+8

\int ln (x) + sin (x) + 8 d x

x ln (x) + 7 x - cos (x) + C

Solution steps

\int ln (x) + sin (x) + 8 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 (x) d x + \int 8 d x

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

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

\int 8 d x = 8 x

= x ln (x) - x - cos (x) + 8 x

Simplify

= x ln (x) + 7 x - cos (x)

Add a constant to the solution

= x ln (x) + 7 x - cos (x) + C

What is the integral of ln(x)+sin(x)+8 ?
The integral of ln(x)+sin(x)+8 is xln(x)+7x-cos(x)+C