Calculus Examples

$\frac{d x}{\cos^{2} (x)}$

Step 1

Since $\frac{x}{\cos^{2} (x)}$ is constant with respect to $d$ , move $\frac{x}{\cos^{2} (x)}$ out of the integral.

$\frac{x}{\cos^{2} (x)} \int d d \cdot d$

Step 2

By the Power Rule, the integral of $d$ with respect to $d$ is $\frac{1}{2} d^{2}$ .

$\frac{x}{\cos^{2} (x)} (\frac{1}{2} d^{2} + C)$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $\frac{x}{\cos^{2} (x)} (\frac{1}{2} d^{2} + C)$ as $\frac{x}{1} \sec^{2} (x) (\frac{1}{2} d^{2}) + C$ .

$\frac{x}{1} \sec^{2} (x) (\frac{1}{2} d^{2}) + C$

Step 3.2

Simplify.

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Step 3.2.1

Divide $x$ by $1$ .

$x \sec^{2} (x) (\frac{1}{2} d^{2}) + C$

Step 3.2.2

Combine $\frac{1}{2}$ and $d^{2}$ .

$x \sec^{2} (x) \frac{d^{2}}{2} + C$

Step 3.2.3

Combine $\frac{d^{2}}{2}$ and $x$ .

$\frac{d^{2} x}{2} \sec^{2} (x) + C$

Step 3.2.4

Combine $\frac{d^{2} x}{2}$ and $\sec^{2} (x)$ .

$\frac{d^{2} x \sec^{2} (x)}{2} + C$

$\frac{1}{2} d^{2} x \sec^{2} (x) + C$