What is the integral of (x+cos(x))' ?

The integral of (x+cos(x))' is x(x+cos(x))'+xsin(x)+cos(x)+C

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integral of (x+cos(x))'

\int (x + cos (x))^{'} d x

x (x + cos (x))' + x sin (x) + cos (x) + C

Solution steps

\int (x + cos (x))^{'} d x

Apply Integration By Parts

: x (x + cos (x))^{'} - \int - x cos (x) d x

= x (x + cos (x))^{^{'}} - \int - x cos (x) d x

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

= x (x + cos (x))^{^{'}} - (- x sin (x) - cos (x))

Simplify

= x (x + cos (x))^{^{'}} + x sin (x) + cos (x)

Add a constant to the solution

= x (x + cos (x))^{^{'}} + x sin (x) + cos (x) + C

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What is the integral of (x+cos(x))' ?
The integral of (x+cos(x))' is x(x+cos(x))'+xsin(x)+cos(x)+C