What is the integral of (2x)cos(x) ?

The integral of (2x)cos(x) is 2(xsin(x)+cos(x))+C

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integral of (2x)cos(x)

\int (2 x) cos (x) d x

2 (x sin (x) + cos (x)) + C

Solution steps

\int 2 x cos (x) d x

Take the constant out:

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

= 2 \cdot \int x cos (x) d x

Apply Integration By Parts

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

= 2 (x sin (x) - \int sin (x) d x)

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

= 2 (x sin (x) - (- cos (x)))

Simplify

= 2 (x sin (x) + cos (x))

Add a constant to the solution

= 2 (x sin (x) + cos (x)) + C

tan (x), 0, 1, 2, 3, \frac{π}{4}

y = 7 x, y = 6 x^{2}

x = 0, y = 2, y = x

(sin (t) - t cos (t))^{^{'}}

What is the integral of (2x)cos(x) ?
The integral of (2x)cos(x) is 2(xsin(x)+cos(x))+C