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Find the integral $\int\frac{y^{\frac{7}{2}}-y^{\frac{5}{3}}-\sqrt[4]{y}}{y^2}dy$

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Final Answer

$\frac{2}{5}\sqrt{y^{5}}-\frac{3}{2}\sqrt[3]{y^{2}}+\frac{4}{3\sqrt[4]{y^{3}}}+C_0$
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Step-by-step Solution

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Simplifying

$\int\frac{\sqrt{y^{7}}-\sqrt[3]{y^{5}}-\sqrt[4]{y}}{y^2}dy$

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$\int\frac{\sqrt{y^{7}}-\sqrt[3]{y^{5}}-\sqrt[4]{y}}{y^2}dy$

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Learn how to solve problems step by step online. Find the integral int((y^(7/2)-y^(5/3)-y^1/4)/(y^2))dy. Simplifying. Expand the fraction \frac{\sqrt{y^{7}}-\sqrt[3]{y^{5}}-\sqrt[4]{y}}{y^2} into 3 simpler fractions with common denominator y^2. Simplify the resulting fractions. Expand the integral \int\left(\sqrt{y^{3}}+\frac{-1}{\sqrt[3]{y}}+\frac{-1}{\sqrt[4]{y^{7}}}\right)dy into 3 integrals using the sum rule for integrals, to then solve each integral separately.

Final Answer

$\frac{2}{5}\sqrt{y^{5}}-\frac{3}{2}\sqrt[3]{y^{2}}+\frac{4}{3\sqrt[4]{y^{3}}}+C_0$

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Function Plot

Plotting: $\frac{2}{5}\sqrt{y^{5}}-\frac{3}{2}\sqrt[3]{y^{2}}+\frac{4}{3\sqrt[4]{y^{3}}}+C_0$

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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