Calculus Examples

$\int \frac{1}{{(z^{2} - 2 z + 5)}^{2}} d x$

Step 1

Apply the constant rule.

$\frac{1}{{(z^{2} - 2 z + 5)}^{2}} x + C$

Step 2

Simplify the answer.

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Step 2.1

Combine $\frac{1}{{(z^{2} - 2 z + 5)}^{2}}$ and $x$ .

$\frac{x}{{(z^{2} - 2 z + 5)}^{2}} + C$

Step 2.2

Rewrite $\frac{x}{{(z^{2} - 2 z + 5)}^{2}} + C$ as $\frac{x}{(z^{2} - 2 z + 5) (z^{2} - 2 z + 5)} + C$ .

$\frac{x}{(z^{2} - 2 z + 5) (z^{2} - 2 z + 5)} + C$

Step 2.3

Simplify.

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Step 2.3.1

Raise $z^{2} - 2 z + 5$ to the power of $1$ .

$\frac{x}{{(z^{2} - 2 z + 5)}^{1} (z^{2} - 2 z + 5)} + C$

Step 2.3.2

Raise $z^{2} - 2 z + 5$ to the power of $1$ .

$\frac{x}{{(z^{2} - 2 z + 5)}^{1} {(z^{2} - 2 z + 5)}^{1}} + C$

Step 2.3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x}{{(z^{2} - 2 z + 5)}^{1 + 1}} + C$

Step 2.3.4

Add $1$ and $1$ .

$\frac{x}{{(z^{2} - 2 z + 5)}^{2}} + C$