Calculus Examples

$\int x f (x) d x$

Step 1

Simplify.

Tap for more steps...

Step 1.1

Raise $x$ to the power of $1$ .

$\int f (x^{1} x) d x$

Step 1.2

Raise $x$ to the power of $1$ .

$\int f (x^{1} x^{1}) d x$

Step 1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\int f x^{1 + 1} d x$

Step 1.4

Add $1$ and $1$ .

$\int f x^{2} d x$

Step 2

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

$f \int x^{2} d x$

Step 3

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

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

Step 4

Simplify the answer.

Tap for more steps...

Step 4.1

Rewrite $f (\frac{1}{3} x^{3} + C)$ as $f \frac{1}{3} x^{3} + C$ .

$f \frac{1}{3} x^{3} + C$

Step 4.2

Simplify.

Tap for more steps...

Step 4.2.1

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

$\frac{f}{3} x^{3} + C$

Step 4.2.2

Combine $\frac{f}{3}$ and $x^{3}$ .

$\frac{f x^{3}}{3} + C$

$\frac{1}{3} f x^{3} + C$