Calculus Examples

$\int_{0}^{1} \frac{3 x^{3} - x^{2} + 2 x - 4}{\sqrt{x^{2}} - 3 x + 2} d x$

Step 1

This derivative could not be completed using the chain rule. Mathway will use another method.

Step 2

Simplify by adding terms.

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Step 2.1

Pull terms out from under the radical, assuming positive real numbers.

$\frac{d}{d x} [\int_{0}^{1} \frac{3 x^{3} - x^{2} + 2 x - 4}{x - 3 x + 2} d x]$

Step 2.2

Subtract $3 x$ from $x$ .

$\frac{d}{d x} [\int_{0}^{1} \frac{3 x^{3} - x^{2} + 2 x - 4}{- 2 x + 2} d x]$

Step 3

Once $\int_{0}^{1} \frac{3 x^{3} - x^{2} + 2 x - 4}{- 2 x + 2} d x$ has been evaluated, it will be constant with respect to $x$ , so the derivative of $\int_{0}^{1} \frac{3 x^{3} - x^{2} + 2 x - 4}{- 2 x + 2} d x$ with respect to $x$ is $0$ .

$0$