What is the integral of arctan(6t) ?

The integral of arctan(6t) is tarctan(6t)-1/12 ln|36t^2+1|+C

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integral of arctan(6t)

\int arctan (6 t) d t

t arctan (6 t) - \frac{1}{12} ln 36 t^{2} + 1 + C

Solution steps

\int arctan (6 t) d t

Apply Integration By Parts

: t arctan (6 t) - \int \frac{6 t}{36 t ^{2} + 1} d t

= t arctan (6 t) - \int \frac{6 t}{36 t ^{2} + 1} d t

\int \frac{6 t}{36 t ^{2} + 1} d t = \frac{1}{12} ln 36 t^{2} + 1

= t arctan (6 t) - \frac{1}{12} ln 36 t^{2} + 1

Add a constant to the solution

= t arctan (6 t) - \frac{1}{12} ln 36 t^{2} + 1 + C

\frac{d y}{d x}, (x y)^{\frac{1}{2}} = 1 + x^{2} y

y^{^{''}} + 4 y^{^{'}} + 4 y = \frac{ln ( t )}{t} e^{- 2 t}

(e^{x})^{2}

\int \frac{27}{w ^{2} 9 - w ^{2}} d w

\int \frac{( e ^{- x} + 6 ) ^{2}}{e ^{x}} d x

What is the integral of arctan(6t) ?
The integral of arctan(6t) is tarctan(6t)-1/12 ln|36t^2+1|+C