What is the integral of arctan(8t) ?

The integral of arctan(8t) is tarctan(8t)-1/16 ln|64t^2+1|+C

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integral of arctan(8t)

\int arctan (8 t) d t

t arctan (8 t) - \frac{1}{16} ln 64 t^{2} + 1 + C

Solution steps

\int arctan (8 t) d t

Apply Integration By Parts

: t arctan (8 t) - \int \frac{8 t}{64 t ^{2} + 1} d t

= t arctan (8 t) - \int \frac{8 t}{64 t ^{2} + 1} d t

\int \frac{8 t}{64 t ^{2} + 1} d t = \frac{1}{16} ln 64 t^{2} + 1

= t arctan (8 t) - \frac{1}{16} ln 64 t^{2} + 1

Add a constant to the solution

= t arctan (8 t) - \frac{1}{16} ln 64 t^{2} + 1 + C

(3 x y + 3 y - 4) d x + (x + 1)^{2} d y = 0

n = 0 \sum \infty n e^{- 8 n}

\frac{\partial}{\partial x} (e^{2 x - 3 y})

\frac{d}{d x} ((\frac{x ^{2} + 3}{x ^{2} - 3})^{4})

\frac{\partial}{\partial x} (\frac{x}{A})

What is the integral of arctan(8t) ?
The integral of arctan(8t) is tarctan(8t)-1/16 ln|64t^2+1|+C