What is the integral of arctan(9t) ?

The integral of arctan(9t) is tarctan(9t)-1/18 ln|81t^2+1|+C

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integral of arctan(9t)

\int arctan (9 t) d t

t arctan (9 t) - \frac{1}{18} ln 81 t^{2} + 1 + C

Solution steps

\int arctan (9 t) d t

Apply Integration By Parts

: t arctan (9 t) - \int \frac{9 t}{81 t ^{2} + 1} d t

= t arctan (9 t) - \int \frac{9 t}{81 t ^{2} + 1} d t

\int \frac{9 t}{81 t ^{2} + 1} d t = \frac{1}{18} ln 81 t^{2} + 1

= t arctan (9 t) - \frac{1}{18} ln 81 t^{2} + 1

Add a constant to the solution

= t arctan (9 t) - \frac{1}{18} ln 81 t^{2} + 1 + C

\frac{d y}{d x} + y^{7} x + 6 y = 0

(- 1, 1), (2, - 11)

\frac{d}{d x} (e^{x^{4}} + lo g_{3} (π))

x \to - 2 lim (x^{2} - 2 x + 4)

\frac{\partial}{\partial x} (y (2 - x - y))

What is the integral of arctan(9t) ?
The integral of arctan(9t) is tarctan(9t)-1/18 ln|81t^2+1|+C