What is the integral of ln^x(x ?

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

integral of ln^x(x

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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