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Let’s check out your problem:
∫
y
(
1
−
1
y
)
d
y
\int \sqrt{y}\left(1-\frac{1}{y}\right) d y
∫
y
(
1
−
y
1
)
d
y
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Math Problems
Algebra 1
Evaluate integers raised to rational exponents
Full solution
Q.
∫
y
(
1
−
1
y
)
d
y
\int \sqrt{y}\left(1-\frac{1}{y}\right) d y
∫
y
(
1
−
y
1
)
d
y
Identify integral:
Identify the integral to be solved.
\newline
∫
1
−
1
y
d
y
\int\sqrt{1 - \frac{1}{y}} \, dy
∫
1
−
y
1
d
y
Simplify expression:
Simplify the expression under the
square root
.
\newline
Let
u
=
1
−
1
y
u = 1 - \frac{1}{y}
u
=
1
−
y
1
, then
d
u
=
1
y
2
d
y
du = \frac{1}{y^2} dy
d
u
=
y
2
1
d
y
Substitute
u
u
u
and
d
u
du
d
u
:
Substitute
u
u
u
and
d
u
du
d
u
into the integral.
\newline
∫
u
⋅
y
2
d
u
\int \sqrt{u} \cdot y^{2} \, du
∫
u
⋅
y
2
d
u
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\newline
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