What is the integral of x^2cos(1/4 x) ?

The integral of x^2cos(1/4 x) is 4x^2sin(1/4 x)-8(-4xcos(1/4 x)+16sin(1/4 x))+C

integral of x^2cos(1/4 x)

\int x^{2} cos (\frac{1}{4} x) d x

4 x^{2} sin (\frac{1}{4} x) - 8 (- 4 x cos (\frac{1}{4} x) + 16 sin (\frac{1}{4} x)) + C

Solution steps

\int x^{2} cos (\frac{1}{4} x) d x

Apply Integration By Parts

= 4 x^{2} sin (\frac{1}{4} x) - \int 8 x sin (\frac{1}{4} x) d x

\int 8 x sin (\frac{1}{4} x) d x = 8 (- 4 x cos (\frac{1}{4} x) + 16 sin (\frac{1}{4} x))

= 4 x^{2} sin (\frac{1}{4} x) - 8 (- 4 x cos (\frac{1}{4} x) + 16 sin (\frac{1}{4} x))

Add a constant to the solution

= 4 x^{2} sin (\frac{1}{4} x) - 8 (- 4 x cos (\frac{1}{4} x) + 16 sin (\frac{1}{4} x)) + C

s l o p e (16, 1.2), (32, 2.4)

\int x^{2} \cdot arctan (x) d x

\int_{1}^{x} t^{2} d t

s l o p e x y - 8 y^{2} = 4, (18, 2)

l a pl a ce t r an s f or m 5 + 2 t cos (2 t)

What is the integral of x^2cos(1/4 x) ?
The integral of x^2cos(1/4 x) is 4x^2sin(1/4 x)-8(-4xcos(1/4 x)+16sin(1/4 x))+C