What is the integral of (sin(x))' ?

The integral of (sin(x))' is x(sin(x))'-xcos(x)+sin(x)+C

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integral of (sin(x))'

\int (sin (x))^{'} d x

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

Solution steps

\int (sin (x))^{'} d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int \frac{4 x ^{2} - 5 x - 15}{x ^{3} - 4 x ^{2} - 5 x} d x

\int e^{3 t a n (x)} sec^{2} (x) d x

\int \frac{2 x ^{2} + x}{x ^{4} - 2 x ^{2} + 1} d x

\int cos (x) cos (2 sin (x)) d x

\int - x^{2} + 3 x + 4 d x

What is the integral of (sin(x))' ?
The integral of (sin(x))' is x(sin(x))'-xcos(x)+sin(x)+C