What is the integral of f(x)=2xcos(x) ?

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

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integral of f(x)=2xcos(x)

integral

f (x) = 2 x cos (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

\frac{1}{( a ^{x} + 1 )}

(x + 2)^{2}

e^{\frac{- 2}{x}}

\frac{[ ln ( ( 2 x ) ^{2} ) ]}{x}

(x^{2} + 1) cos^{2} (x)

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