Calculus Examples

$\int_{1}^{5} x \sqrt{7 x^{2} + 3} d x$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 x^{2} + 3}$ as ${(7 x^{2} + 3)}^{\frac{1}{2}}$ .

$\frac{d}{d x} [\int_{1}^{5} x {(7 x^{2} + 3)}^{\frac{1}{2}} d x]$

Step 2

Once $\int_{1}^{5} x {(7 x^{2} + 3)}^{\frac{1}{2}} d x$ has been evaluated, it will be constant with respect to $x$ , so the derivative of $\int_{1}^{5} x {(7 x^{2} + 3)}^{\frac{1}{2}} d x$ with respect to $x$ is $0$ .

$0$