Mathematics, 02.06.2021 07:50 payshencec21
Determine the following indefinite integrals. Check your work by differentiation. ∫4x^1/3-x^-1/3dx
Answers: 3
![4∫\sqrt[3]{x} \: dx - ∫ \frac{dx}{ \sqrt[3]{x} }](/tpl/images/1358/8563/bcbfe.png)
![∫ \sqrt[3]{x} \: dx = \frac{3}{4} \sqrt[3]{ {x}^{4} } + c](/tpl/images/1358/8563/3b1d2.png)
![∫ \frac{dx}{ \sqrt[3]{x} } = \frac{3}{2} \sqrt[3]{ {x}^{2} } + c](/tpl/images/1358/8563/892fe.png)
![∫(4\sqrt[3]{x} - \frac{1}{ \sqrt[3]{x} } )dx](/tpl/images/1358/8563/a9057.png)
![= 3 \sqrt[3]{ {x}^{4} } \: - \frac{3}{2} \sqrt[3]{ {x}^{2} } + k](/tpl/images/1358/8563/7efbd.png)
![\frac{d}{dx} (3 \sqrt[3]{ {x}^{4} } \: - \frac{3}{2} \sqrt[3]{ {x}^{2} } + k)](/tpl/images/1358/8563/48e35.png)
![= 3( \frac{4}{3} ) \sqrt[3]{x} \: \: - ( \frac{3}{2} )( \frac{2}{3} ) (\frac{1}{ \sqrt[3]{x} } )](/tpl/images/1358/8563/4a116.png)
![= 4\sqrt[3]{x} - \frac{1}{ \sqrt[3]{x} }](/tpl/images/1358/8563/233ee.png)
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Determine the following indefinite integrals. Check your work by differentiation.
∫4x^1/3-x^-1/3dx...
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