Question

Integrate with respect to x :
∫41 x+1/x√x dx
note 41 means that 4 superscript, 1subcript

203
20
320
-20

Answer 1

Answer on Question #46127 – Math - Integral Calculus

Integrate with respect to $x$ :

$$\int_{1}^{4} (x + \frac{1}{x\sqrt{x}}) dx$$

Solution.

$$\begin{aligned} \int_{1}^{4} \left(x + \frac{1}{x\sqrt{x}}\right) dx &= \int_{1}^{4} (x + x^{-\frac{3}{2}}) dx = \\ &= \left\{\frac{x^2}{2} + x^{-\frac{1}{2}}(-2)\right\} \Big|_{1}^{4} = \left\{8 - \frac{1}{2} - \frac{2}{2} + \frac{2}{1}\right\} = \left\{8 - \frac{1}{2} - 1 + 2\right\} = 9 - \frac{1}{2} = \frac{18 - 1}{2} = \frac{17}{2} \end{aligned}$$

Answer: $\frac{17}{2}$

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