Find the integral $\int\frac{1}{\frac{3}{2}\left(x^2-4x+4\right)}dx$

Step-by-step Solution

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Final answer to the problem

$\frac{-2}{3\left(x-2\right)}+C_0$
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Step-by-step Solution

How should I solve this problem?

  • Integrate using trigonometric identities
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
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1

Divide fractions $\frac{1}{\frac{3}{2}\left(x^2-4x+4\right)}$ with Keep, Change, Flip: $a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}$

$\int\frac{2}{3\left(x^2-4x+4\right)}dx$

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$\int\frac{2}{3\left(x^2-4x+4\right)}dx$

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Learn how to solve problems step by step online. Find the integral int(1/((x^2-4x+4)3/2))dx. Divide fractions \frac{1}{\frac{3}{2}\left(x^2-4x+4\right)} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. The trinomial \left(x^2-4x+4\right) is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial.

Final answer to the problem

$\frac{-2}{3\left(x-2\right)}+C_0$

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Function Plot

Plotting: $\frac{-2}{3\left(x-2\right)}+C_0$

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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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