What is the integral of xcos(21x) ?

The integral of xcos(21x) is 1/441 (21xsin(21x)+cos(21x))+C

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integral of xcos(21x)

\int x cos (21 x) d x

\frac{1}{441} (21 x sin (21 x) + cos (21 x)) + C

Solution steps

\int x cos (21 x) d x

Apply u-substitution

: \int \frac{u cos ( u )}{441} d u

= \int \frac{u cos ( u )}{441} d u

Take the constant out:

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

= \frac{1}{441} \cdot \int u cos (u) d u

Apply Integration By Parts

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

= \frac{1}{441} (u sin (u) - \int sin (u) d u)

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

= \frac{1}{441} (u sin (u) - (- cos (u)))

Substitute back

u = 21 x

= \frac{1}{441} (21 x sin (21 x) - (- cos (21 x)))

Simplify

= \frac{1}{441} (21 x sin (21 x) + cos (21 x))

Add a constant to the solution

= \frac{1}{441} (21 x sin (21 x) + cos (21 x)) + C

\int x^{2} e^{- x^{3}} sin^{2} (x^{3}) d x

\frac{\partial}{\partial x} (sin (y - 5 x))

x \to \frac{π}{2} lim (7 e^{- 2})

x^{^{''}} + 2 x^{^{'}} + 2 x = 0, x (0) = 0, x^{^{'}} (0) = 1

What is the integral of xcos(21x) ?
The integral of xcos(21x) is 1/441 (21xsin(21x)+cos(21x))+C