What is the integral of 6xcos(x) ?

The integral of 6xcos(x) is 6(xsin(x)+cos(x))+C

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integral of 6xcos(x)

\int 6 x cos (x) d x

6 (x sin (x) + cos (x)) + C

Solution steps

\int 6 x cos (x) d x

Take the constant out:

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

= 6 \cdot \int x cos (x) d x

Apply Integration By Parts

= 6 (x sin (x) - \int sin (x) d x)

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

= 6 (x sin (x) - (- cos (x)))

Simplify

= 6 (x sin (x) + cos (x))

Add a constant to the solution

= 6 (x sin (x) + cos (x)) + C

t a y l or φ^{3} cos (φ^{4})

\frac{d}{d x} (25 x^{2})

\frac{d}{d x} (sin (1.5 x))

\frac{d}{d x} (k e^{k x})

\frac{d y}{d x} - \frac{y}{x} = - x e^{- x}

What is the integral of 6xcos(x) ?
The integral of 6xcos(x) is 6(xsin(x)+cos(x))+C