What is the integral of 1/(z^2sqrt(a^2+x^2)) ?

The integral of 1/(z^2sqrt(a^2+x^2)) is -1/(zsqrt(a^2+x^2))+C

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integral of 1/(z^2sqrt(a^2+x^2))

\int \frac{1}{z ^{2} a ^{2} + x ^{2}} d z

- \frac{1}{z a ^{2} + x ^{2}} + C

Solution steps

\int \frac{1}{z ^{2} a ^{2} + x ^{2}} d z

Take the constant out:

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

= \frac{1}{a ^{2} + x ^{2}} \cdot \int \frac{1}{z ^{2}} d z

Apply the Power Rule

= \frac{1}{a ^{2} + x ^{2}} (- \frac{1}{z})

Simplify

\frac{1}{a ^{2} + x ^{2}} (- \frac{1}{z}) : - \frac{1}{z a ^{2} + x ^{2}}

= - \frac{1}{z a ^{2} + x ^{2}}

Add a constant to the solution

= - \frac{1}{z a ^{2} + x ^{2}} + C

What is the integral of 1/(z^2sqrt(a^2+x^2)) ?
The integral of 1/(z^2sqrt(a^2+x^2)) is -1/(zsqrt(a^2+x^2))+C