What is the integral of 1/(x(ln(x))^pi) ?

The integral of 1/(x(ln(x))^pi) is (ln^{-pi+1}(x))/(-pi+1)+C

Popular >

integral of 1/(x(ln(x))^pi)

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

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

Solution steps

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

Simplify

= \int \frac{1}{x ln ^{π} ( x )} d x

Apply u-substitution

: \int \frac{1}{u ^{π}} d u

= \int \frac{1}{u ^{π}} d u

Apply the Power Rule

: \frac{u ^{- π + 1}}{- π + 1}

= \frac{u ^{- π + 1}}{- π + 1}

Substitute back

u = ln (x)

= \frac{ln ^{- π + 1} ( x )}{- π + 1}

Add a constant to the solution

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

n = 0 \sum \infty (- 1)^{n} 2^{n}

\int \frac{1}{t ^{2} 121 - t ^{2}} d t

\int e^{2 x} \cdot x^{2} d x

\frac{\partial}{\partial x} (4 (y^{2} - x^{2}) ln (x + y))

\int x^{2} \cdot 1 - x d x

What is the integral of 1/(x(ln(x))^pi) ?
The integral of 1/(x(ln(x))^pi) is (ln^{-pi+1}(x))/(-pi+1)+C