What is the integral of arctan(x/4) ?

The integral of arctan(x/4) is xarctan(x/4)-2ln|x^2+16|+C

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integral of arctan(x/4)

\int arctan (\frac{x}{4}) d x

x arctan (\frac{x}{4}) - 2 ln x^{2} + 16 + C

Solution steps

\int arctan (\frac{x}{4}) d x

Apply Integration By Parts

: x arctan (\frac{x}{4}) - \int \frac{4 x}{x ^{2} + 16} d x

= x arctan (\frac{x}{4}) - \int \frac{4 x}{x ^{2} + 16} d x

\int \frac{4 x}{x ^{2} + 16} d x = 2 ln x^{2} + 16

= x arctan (\frac{x}{4}) - 2 ln x^{2} + 16

Add a constant to the solution

= x arctan (\frac{x}{4}) - 2 ln x^{2} + 16 + C

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

\int 3 sin (t) d t

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

\int 3 sin^{2} (t) d t

y^{^{'''}} + 6 y^{^{''}} + 11 y^{^{'}} + 6 y = 0

What is the integral of arctan(x/4) ?
The integral of arctan(x/4) is xarctan(x/4)-2ln|x^2+16|+C