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\int\frac{y^{\frac{7}{2}}-y^{\frac{5}{3}}-y^{\frac{1}{4}}}{y^2}dy

Integral of (-1y^(5/3)-1y^(1/4)+y^(7/2))/(y^2)

Answer

$-\frac{7}{4}\ln\left(y\right)+\int\frac{-1}{\sqrt[3]{y}}dy+\frac{2}{5}\sqrt{y^{5}}$

Step-by-step explanation

Problem

$\int\frac{y^{\frac{7}{2}}-y^{\frac{5}{3}}-y^{\frac{1}{4}}}{y^2}dy$
1

Split the fraction $\frac{\sqrt{y^{7}}-\sqrt[3]{y^{5}}+-\sqrt[4]{y}}{y^2}$ in two terms with same denominator

$\int\left(\frac{-\sqrt[4]{y}}{y^2}+\frac{\sqrt{y^{7}}-\sqrt[3]{y^{5}}}{y^2}\right)dy$

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Answer

$-\frac{7}{4}\ln\left(y\right)+\int\frac{-1}{\sqrt[3]{y}}dy+\frac{2}{5}\sqrt{y^{5}}$
$\int\frac{y^{\frac{7}{2}}-y^{\frac{5}{3}}-y^{\frac{1}{4}}}{y^2}dy$

Main topic:

Integration by substitution

Used formulas:

2. See formulas

Time to solve it:

~ 1.74 seconds