What is the integral of 6arctan(8/x) ?

The integral of 6arctan(8/x) is 6(xarctan(8/x)+4ln|64+x^2|)+C

integral of 6arctan(8/x)

\int 6 arctan (\frac{8}{x}) d x

6 (x arctan (\frac{8}{x}) + 4 ln 64 + x^{2}) + C

Solution steps

\int 6 arctan (\frac{8}{x}) d x

Take the constant out:

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

= 6 \cdot \int arctan (\frac{8}{x}) d x

Apply Integration By Parts

= 6 (x arctan (\frac{8}{x}) - \int - \frac{8 x}{64 + x ^{2}} d x)

\int - \frac{8 x}{64 + x ^{2}} d x = - 4 ln 64 + x^{2}

= 6 (x arctan (\frac{8}{x}) - (- 4 ln 64 + x^{2}))

Simplify

= 6 (x arctan (\frac{8}{x}) + 4 ln 64 + x^{2})

Add a constant to the solution

= 6 (x arctan (\frac{8}{x}) + 4 ln 64 + x^{2}) + C

y = x^{0.3}

x \to 1 - lim (\frac{2 x - 3}{x - 1})

\frac{d}{d x} (6 cos^{3} (x))

\int 11 + 5 e^{6 - 3 x} - 16 d x

\frac{d}{d x} (x (49 - x^{2})^{\frac{1}{2}})

What is the integral of 6arctan(8/x) ?
The integral of 6arctan(8/x) is 6(xarctan(8/x)+4ln|64+x^2|)+C