What is the integral of 4x^2cos(x/5) ?

The integral of 4x^2cos(x/5) is 4(5x^2sin(x/5)-10(-5xcos(x/5)+25sin(x/5)))+C

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integral of 4x^2cos(x/5)

\int 4 x^{2} cos (\frac{x}{5}) d x

4 (5 x^{2} sin (\frac{x}{5}) - 10 (- 5 x cos (\frac{x}{5}) + 25 sin (\frac{x}{5}))) + C

Solution steps

\int 4 x^{2} cos (\frac{x}{5}) d x

Take the constant out:

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

= 4 \cdot \int x^{2} cos (\frac{x}{5}) d x

Apply Integration By Parts

: 5 x^{2} sin (\frac{x}{5}) - \int 10 x sin (\frac{x}{5}) d x

= 4 (5 x^{2} sin (\frac{x}{5}) - \int 10 x sin (\frac{x}{5}) d x)

\int 10 x sin (\frac{x}{5}) d x = 10 (- 5 x cos (\frac{x}{5}) + 25 sin (\frac{x}{5}))

= 4 (5 x^{2} sin (\frac{x}{5}) - 10 (- 5 x cos (\frac{x}{5}) + 25 sin (\frac{x}{5})))

Add a constant to the solution

= 4 (5 x^{2} sin (\frac{x}{5}) - 10 (- 5 x cos (\frac{x}{5}) + 25 sin (\frac{x}{5}))) + C

x \to 3 - lim (\frac{2}{( x - 3 ) ^{3}})

\int \frac{x - 5}{x + 3} d x

y = (x - 2)^{2}, y = x

f (x) = arcsin (3 x)

f (x) = 2 x (x^{2} + 1)

What is the integral of 4x^2cos(x/5) ?
The integral of 4x^2cos(x/5) is 4(5x^2sin(x/5)-10(-5xcos(x/5)+25sin(x/5)))+C