Calculus Examples

$f (x) = \frac{8 + t + t^{2}}{\sqrt{t}}$

Step 1

The function $F (x)$ can be found by finding the indefinite integral of the derivative $f (x)$ .

$F (x) = \int f (x) d x$

Step 2

Set up the integral to solve.

$F (x) = \int \frac{8 + t + t^{2}}{\sqrt{t}} d x$

Step 3

Apply the constant rule.

$\frac{8 + t + t^{2}}{\sqrt{t}} x + C$

Step 4

Simplify the answer.

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Step 4.1

Combine $\frac{8 + t + t^{2}}{\sqrt{t}}$ and $x$ .

$\frac{(8 + t + t^{2}) x}{\sqrt{t}} + C$

Step 4.2

Rewrite $\frac{(8 + t + t^{2}) x}{\sqrt{t}} + C$ as $\frac{8 x + t x + t^{2} x}{\sqrt{t}} + C$ .

$\frac{8 x + t x + t^{2} x}{\sqrt{t}} + C$

Step 5

The answer is the antiderivative of the function $f (x) = \frac{8 + t + t^{2}}{\sqrt{t}}$ .

$F (x) =$ $\frac{8 x + t x + t^{2} x}{\sqrt{t}} + C$