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

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

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integral of rivative of sin(x)

\int \frac{d}{d x} (sin (x)) d x

x \frac{d}{d x} (sin (x)) - x cos (x) + sin (x) + C

Solution steps

\int \frac{d}{d x} (sin (x)) d x

Apply Integration By Parts

: x \frac{d}{d x} (sin (x)) - \int - x sin (x) d x

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

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

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

Simplify

= x \frac{d}{d x} (sin (x)) - x cos (x) + sin (x)

Add a constant to the solution

= x \frac{d}{d x} (sin (x)) - x cos (x) + sin (x) + C

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\int \frac{1}{x ^{3} - 8 x ^{2} + 21 x - 18} d x

\int \frac{2 x ^{2} + 2 x - 9}{x ^{2} - 4} d x

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