What is the integral of (nx)^{(1-n)/n} ?

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

Popular >

integral of (nx)^{(1-n)/n}

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

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

Solution steps

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

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

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply the Power Rule

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

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

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

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

Add a constant to the solution

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

\int \frac{x}{8 + 2 x - x ^{2}} d x

x \to 0 + lim (x^{1 - c o s (x)})

x \to + 0 + lim (\frac{e ^{x} - 1}{x})

\frac{\partial}{\partial y} (\frac{x z}{x ^{2} + y ^{2}})

\frac{7}{( s - 1 ) ^{3}}

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