What is the integral of pi/2-arctan(x) ?

The integral of pi/2-arctan(x) is pi/2 x-xarctan(x)+1/2 ln|x^2+1|+C

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integral of pi/2-arctan(x)

\int \frac{π}{2} - arctan (x) d x

\frac{π}{2} x - x arctan (x) + \frac{1}{2} ln x^{2} + 1 + C

Solution steps

\int \frac{π}{2} - arctan (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{π}{2} d x - \int arctan (x) d x

\int \frac{π}{2} d x = \frac{π}{2} x

\int arctan (x) d x = x arctan (x) - \frac{1}{2} ln x^{2} + 1

= \frac{π}{2} x - (x arctan (x) - \frac{1}{2} ln x^{2} + 1)

Simplify

= \frac{π}{2} x - x arctan (x) + \frac{1}{2} ln x^{2} + 1

Add a constant to the solution

= \frac{π}{2} x - x arctan (x) + \frac{1}{2} ln x^{2} + 1 + C

y = cot^{2} (cos (θ))

\int_{6}^{\infty} x e^{- 3 x} d x

\frac{d}{d x} (\frac{1}{3} x^{3} - x^{2} - 3 x + 4)

7 x^{4} - 7 x^{2}, 8 x^{2}, 0

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

What is the integral of pi/2-arctan(x) ?
The integral of pi/2-arctan(x) is pi/2 x-xarctan(x)+1/2 ln|x^2+1|+C