What is the integral of 1/(x^n(1+x^n)^{1/n)} ?

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

Popular >

integral of 1/(x^n(1+x^n)^{1/n)}

\int \frac{1}{x ^{n} ( 1 + x ^{n} ) ^{\frac{1}{n}}} d x

\frac{x ^{- n + 1}}{- n + 1} + C

Solution steps

\int \frac{1}{x ^{n} ( 1 + x ^{n} ) ^{\frac{1}{n}}} d x

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{x ^{n} ( 1 + x ^{n} ) ^{\frac{1}{n}}} = x^{- n} \frac{1}{( 1 + ) ^{\frac{1}{n}}}

= \int x^{- n} \frac{1}{( 1 ) ^{\frac{1}{n}}} d x

Simplify

= \int x^{- n} d x

Apply the Power Rule

: \frac{x ^{- n + 1}}{- n + 1}

= \frac{x ^{- n + 1}}{- n + 1}

Add a constant to the solution

= \frac{x ^{- n + 1}}{- n + 1} + C

\int \frac{36}{x ^{2} 36 - x ^{2}} d x

\int \frac{y}{16 - 9 y ^{2}} d y

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

\int tan^{5} (θ) sec^{\frac{9}{2}} (θ) d θ

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