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 \cdot 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

(3, 6), (5, 5)

\frac{d ^{2}}{d x ^{2}} (\frac{6 x ^{5}}{5} - 3 x)

y^{^{''}} - 6 y^{^{'}} + 10 y = 0, y (0) = 3, y^{^{'}} (0) = - 2

7 x^{2} + 4 x - 5

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