What is the integral of xarctan(21x) ?

The integral of xarctan(21x) is 1/2 x^2arctan(21x)-1/882 (-arctan(21x)+21x)+C

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integral of xarctan(21x)

\int x arctan (21 x) d x

\frac{1}{2} x^{2} arctan (21 x) - \frac{1}{882} (- arctan (21 x) + 21 x) + C

Solution steps

\int x arctan (21 x) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} arctan (21 x) - \int \frac{21 x ^{2}}{2 ( 441 x ^{2} + 1 )} d x

= \frac{1}{2} x^{2} arctan (21 x) - \int \frac{21 x ^{2}}{2 ( 441 x ^{2} + 1 )} d x

\int \frac{21 x ^{2}}{2 ( 441 x ^{2} + 1 )} d x = \frac{1}{882} (- arctan (21 x) + 21 x)

= \frac{1}{2} x^{2} arctan (21 x) - \frac{1}{882} (- arctan (21 x) + 21 x)

Add a constant to the solution

= \frac{1}{2} x^{2} arctan (21 x) - \frac{1}{882} (- arctan (21 x) + 21 x) + C

y^{^{'}} - 2 x y = x^{3} y^{5}

(cos (g (x)))^{'}

\int x 9 - x d x

\frac{y ^{2} + x ^{2}}{y ^{2} - x ^{2}}

f (x) = \frac{2}{x}, at x = 1

What is the integral of xarctan(21x) ?
The integral of xarctan(21x) is 1/2 x^2arctan(21x)-1/882 (-arctan(21x)+21x)+C