What is the integral of arctan(2t) ?

The integral of arctan(2t) is tarctan(2t)-1/4 ln|4t^2+1|+C

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integral of arctan(2t)

\int arctan (2 t) d t

t arctan (2 t) - \frac{1}{4} ln 4 t^{2} + 1 + C

Solution steps

\int arctan (2 t) d t

Apply Integration By Parts

: t arctan (2 t) - \int \frac{2 t}{4 t ^{2} + 1} d t

= t arctan (2 t) - \int \frac{2 t}{4 t ^{2} + 1} d t

\int \frac{2 t}{4 t ^{2} + 1} d t = \frac{1}{4} ln 4 t^{2} + 1

= t arctan (2 t) - \frac{1}{4} ln 4 t^{2} + 1

Add a constant to the solution

= t arctan (2 t) - \frac{1}{4} ln 4 t^{2} + 1 + C

f (x) = x^{4} - 8 x^{3}

f (x) = 3 x^{3} - 9 x

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

\int \frac{sin ^{7} ( 11 x )}{cos ^{4} ( 11 x )} d x

y = (6 x + 1)^{2}

What is the integral of arctan(2t) ?
The integral of arctan(2t) is tarctan(2t)-1/4 ln|4t^2+1|+C