What is the integral of-5xcos(x) ?

The integral of-5xcos(x) is -5(xsin(x)+cos(x))+C

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integral of-5xcos(x)

\int - 5 x cos (x) d x

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

Solution steps

\int - 5 x cos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 5 \cdot \int x cos (x) d x

Apply Integration By Parts

: x sin (x) - \int sin (x) d x

= - 5 (x sin (x) - \int sin (x) d x)

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

= - 5 (x sin (x) - (- cos (x)))

Simplify

= - 5 (x sin (x) + cos (x))

Add a constant to the solution

= - 5 (x sin (x) + cos (x)) + C

\frac{d}{d x} ((y - x)^{2})

x \to 2 lim (∣ x - 3 ∣)

\int cos (t) - sin (t) d t

f (x) = x^{3} + x

\frac{d y}{d x} (2 x + y + 1) = 1

What is the integral of-5xcos(x) ?
The integral of-5xcos(x) is -5(xsin(x)+cos(x))+C