Calculus Examples

$\int 4 x - 3^{9} d x$

Step 1

Simplify.

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Step 1.1

Raise $3$ to the power of $9$ .

$\int 4 x - 1 \cdot 19683 d x$

Step 1.2

Multiply $- 1$ by $19683$ .

$\int 4 x - 19683 d x$

Step 2

Split the single integral into multiple integrals.

$\int 4 x d x + \int - 19683 d x$

Step 3

Since $4$ is constant with respect to $x$ , move $4$ out of the integral.

$4 \int x d x + \int - 19683 d x$

Step 4

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

$4 (\frac{1}{2} x^{2} + C) + \int - 19683 d x$

Step 5

Apply the constant rule.

$4 (\frac{1}{2} x^{2} + C) - 19683 x + C$

Step 6

Simplify.

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Step 6.1

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

$4 (\frac{x^{2}}{2} + C) - 19683 x + C$

Step 6.2

Simplify.

$2 x^{2} - 19683 x + C$