Calculus Examples

$(7 x^{3} + 4 x^{2}) d x$

Step 1

Remove parentheses.

$\int 7 x^{3} + 4 x^{2} d x$

Step 2

Split the single integral into multiple integrals.

$\int 7 x^{3} d x + \int 4 x^{2} d x$

Step 3

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

$7 \int x^{3} d x + \int 4 x^{2} d x$

Step 4

By the Power Rule, the integral of $x^{3}$ with respect to $x$ is $\frac{1}{4} x^{4}$ .

$7 (\frac{1}{4} x^{4} + C) + \int 4 x^{2} d x$

Step 5

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

$7 (\frac{1}{4} x^{4} + C) + 4 \int x^{2} d x$

Step 6

By the Power Rule, the integral of $x^{2}$ with respect to $x$ is $\frac{1}{3} x^{3}$ .

$7 (\frac{1}{4} x^{4} + C) + 4 (\frac{1}{3} x^{3} + C)$

Step 7

Simplify.

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Step 7.1

Simplify.

$7 (\frac{1}{4}) x^{4} + 4 (\frac{1}{3}) x^{3} + C$

Step 7.2

Simplify.

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Step 7.2.1

Combine $7$ and $\frac{1}{4}$ .

$\frac{7}{4} x^{4} + 4 (\frac{1}{3}) x^{3} + C$

Step 7.2.2

Combine $4$ and $\frac{1}{3}$ .

$\frac{7}{4} x^{4} + \frac{4}{3} x^{3} + C$