What is the integral of 4xcos(x) ?

The integral of 4xcos(x) is 4(xsin(x)+cos(x))+C

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integral of 4xcos(x)

\int 4 x cos (x) d x

4 (x sin (x) + cos (x)) + C

Solution steps

\int 4 x cos (x) d x

Take the constant out:

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

= 4 \cdot \int x cos (x) d x

Apply Integration By Parts

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

= 4 (x sin (x) - \int sin (x) d x)

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

= 4 (x sin (x) - (- cos (x)))

Simplify

= 4 (x sin (x) + cos (x))

Add a constant to the solution

= 4 (x sin (x) + cos (x)) + C

\int_{- 2}^{3} \frac{3}{x ^{4}} d x

\frac{\partial}{\partial x} (v)

n = 0 \sum \infty (- 1)^{n} x^{3 n}

(x, y) \to (1, 1) lim (x + y)

\int \frac{2 - 4 t ^{2}}{t - t ^{3}} d t

What is the integral of 4xcos(x) ?
The integral of 4xcos(x) is 4(xsin(x)+cos(x))+C