What is the integral of arctan^x(x ?

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

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integral of arctan^x(x

\int arctan^{x} (d) x d x

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

Solution steps

\int arctan^{x} (d) x d x

Apply Integration By Parts

: \frac{x arctan ^{x} ( d )}{ln ( arctan ( d ) )} - \int \frac{arctan ^{x} ( d )}{ln ( arctan ( d ) )} d x

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

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

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

Add a constant to the solution

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

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