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

The integral of rivative of cos(x) is x derivative of cos(x)+xsin(x)+cos(x)+C

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integral of rivative of cos(x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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\int sec^{13} (2 x) tan^{3} (2 x) d x

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