Calculus Examples

$\int 3 x - 7 d x$

Step 1

Split the single integral into multiple integrals.

$\int 3 x d x + \int - 7 d x$

Step 2

Since $3$ is constant with respect to $x$ , move $3$ out of the integral.

$3 \int x d x + \int - 7 d x$

Step 3

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

$3 (\frac{1}{2} x^{2} + C) + \int - 7 d x$

Step 4

Apply the constant rule.

$3 (\frac{1}{2} x^{2} + C) - 7 x + C$

Step 5

Simplify.

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Step 5.1

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

$3 (\frac{x^{2}}{2} + C) - 7 x + C$

Step 5.2

Simplify.

$\frac{3 x^{2}}{2} - 7 x + C$

Step 5.3

Reorder terms.

$\frac{3}{2} x^{2} - 7 x + C$