What is the integral of (5x^4+64)arctan(x/2) ?

The integral of (5x^4+64)arctan(x/2) is arctan(x/2)(x^5+64x)-2((x^4)/4-2x^2+40ln|x^2+4|)+C

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integral of (5x^4+64)arctan(x/2)

\int (5 x^{4} + 64) arctan (\frac{x}{2}) d x

arctan (\frac{x}{2}) (x^{5} + 64 x) - 2 (\frac{x ^{4}}{4} - 2 x^{2} + 40 ln x^{2} + 4) + C

Solution steps

\int (5 x^{4} + 64) arctan (\frac{x}{2}) d x

Apply Integration By Parts

: arctan (\frac{x}{2}) (x^{5} + 64 x) - \int \frac{2 ( x ^{5} + 64 x )}{x ^{2} + 4} d x

= arctan (\frac{x}{2}) (x^{5} + 64 x) - \int \frac{2 ( x ^{5} + 64 x )}{x ^{2} + 4} d x

\int \frac{2 ( x ^{5} + 64 x )}{x ^{2} + 4} d x = 2 (\frac{x ^{4}}{4} - 2 x^{2} + 40 ln x^{2} + 4)

= arctan (\frac{x}{2}) (x^{5} + 64 x) - 2 (\frac{x ^{4}}{4} - 2 x^{2} + 40 ln x^{2} + 4)

Add a constant to the solution

= arctan (\frac{x}{2}) (x^{5} + 64 x) - 2 (\frac{x ^{4}}{4} - 2 x^{2} + 40 ln x^{2} + 4) + C

f (x) = 5 - x

lo g_{10} (\frac{( x + 1 ) ( x - 8 )}{( x - 1 ) ( x + 8 )})

n = 1 \sum \infty \frac{1}{5 ^{n + 1}}

\int 3^{x} + \frac{2}{x} d x

\frac{\partial}{\partial x} (e^{8 x y})

What is the integral of (5x^4+64)arctan(x/2) ?
The integral of (5x^4+64)arctan(x/2) is arctan(x/2)(x^5+64x)-2((x^4)/4-2x^2+40ln|x^2+4|)+C