What is the integral of 9arctan(x) ?

The integral of 9arctan(x) is 9(xarctan(x)-1/2 ln|x^2+1|)+C

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integral of 9arctan(x)

\int 9 arctan (x) d x

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

Solution steps

\int 9 arctan (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \int arctan (x) d x

Apply Integration By Parts

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

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

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

= 9 (x arctan (x) - \frac{1}{2} ln x^{2} + 1)

Add a constant to the solution

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

\frac{\partial}{\partial y} (7 y - 5 x)

x \to \infty lim (lo g_{10} (2 x))

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

\frac{d}{d x} (9 sec (x))

\frac{\partial}{\partial y} (ln (e^{x} + x y^{3}))

What is the integral of 9arctan(x) ?
The integral of 9arctan(x) is 9(xarctan(x)-1/2 ln|x^2+1|)+C