Calculus Examples

$\int (6 x + x) d x$

Step 1

Remove parentheses.

$\int 6 x + x d x$

Step 2

Add $6 x$ and $x$ .

$\int 7 x d x$

Step 3

Since $7$ is constant with respect to $x$ , move $7$ out of the integral.

$7 \int x d x$

Step 4

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

$7 (\frac{1}{2} x^{2} + C)$

Step 5

Simplify the answer.

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Step 5.1

Rewrite $7 (\frac{1}{2} x^{2} + C)$ as $7 (\frac{1}{2}) x^{2} + C$ .

$7 (\frac{1}{2}) x^{2} + C$

Step 5.2

Combine $7$ and $\frac{1}{2}$ .

$\frac{7}{2} x^{2} + C$