Integrate the function $\left(2x\ln\left(x\right)-x^3\right)\sqrt{2x^2+1+x^4}$ from $1$ to $3$

Step-by-step Solution

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Final answer to the problem

$-\frac{466}{3}+\frac{99}{2}\ln\left|3\right|$
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Step-by-step Solution

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  • Integrate by partial fractions
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  • Integrate using tabular integration
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  • Weierstrass Substitution
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  • Integrate using basic integrals
  • Product of Binomials with Common Term
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1

The trinomial $2x^2+1+x^4$ is a perfect square trinomial, because it's discriminant is equal to zero

$\Delta=b^2-4ac=2^2-4\left(1\right)\left(1\right) = 0$

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$\Delta=b^2-4ac=2^2-4\left(1\right)\left(1\right) = 0$

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Learn how to solve problems step by step online. Integrate the function (2xln(x)-x^3)(2x^2+1x^4)^(1/2) from 1 to 3. The trinomial 2x^2+1+x^4 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial. Cancel exponents 2 and 1.

Final answer to the problem

$-\frac{466}{3}+\frac{99}{2}\ln\left|3\right|$

Exact Numeric Answer

$-100.952025$

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Function Plot

Plotting: $\left(2x\ln\left(x\right)-x^3\right)\sqrt{2x^2+1+x^4}$

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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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