What is the integral of ((5t^2+7)/(t^{4/3)}) ?

The integral of ((5t^2+7)/(t^{4/3)}) is 3t^{5/3}-(21)/(t^{1/3)}+C

integral of ((5t^2+7)/(t^{4/3)})

\int (\frac{5 t ^{2} + 7}{t ^{\frac{4}{3}}}) d t

3 t^{\frac{5}{3}} - \frac{21}{t ^{\frac{1}{3}}} + C

Solution steps

\int \frac{5 t ^{2} + 7}{t ^{\frac{4}{3}}} d t

Expand

\frac{5 t ^{2} + 7}{t ^{\frac{4}{3}}} : 5 t^{\frac{2}{3}} + \frac{7}{t ^{\frac{4}{3}}}

= \int 5 t^{\frac{2}{3}} + \frac{7}{t ^{\frac{4}{3}}} d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 5 t^{\frac{2}{3}} d t + \int \frac{7}{t ^{\frac{4}{3}}} d t

\int 5 t^{\frac{2}{3}} d t = 3 t^{\frac{5}{3}}

\int \frac{7}{t ^{\frac{4}{3}}} d t = - \frac{21}{t ^{\frac{1}{3}}}

= 3 t^{\frac{5}{3}} - \frac{21}{t ^{\frac{1}{3}}}

Add a constant to the solution

= 3 t^{\frac{5}{3}} - \frac{21}{t ^{\frac{1}{3}}} + C

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What is the integral of ((5t^2+7)/(t^{4/3)}) ?
The integral of ((5t^2+7)/(t^{4/3)}) is 3t^{5/3}-(21)/(t^{1/3)}+C