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

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

= 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

y = x^{2}, y = 3 x

n = 0 \sum \infty 7^{2}

\frac{d y}{d x} = sin (7 x)

x \to \frac{6}{7} lim (x^{4})

\frac{d}{d x} (3 + 2 x^{\frac{1}{3}})

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