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Find the integral of $\frac{x^5+\left(2\sqrt{3}+2\right)x^3+2\sqrt{2}+7}{x-\sqrt{2}+1}$

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Final answer to the problem

$\frac{x^{5}}{5}+\frac{32}{309}x^{4}+\frac{33}{577}x^{3}+\frac{7}{197}x^2+\frac{33}{1121}x+9.8406204\ln\left(x-0.4142136\right)+C_0$
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Step-by-step Solution

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Find the integral

$\int\frac{x^5+\left(2\sqrt{3}+2\right)x^3+2\sqrt{2}+7}{x-\sqrt{2}+1}dx$

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$\int\frac{x^5+\left(2\sqrt{3}+2\right)x^3+2\sqrt{2}+7}{x-\sqrt{2}+1}dx$

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Learn how to solve integral calculus problems step by step online. Find the integral of (x^5+(23^1/2+2)x^322^1/2+7)/(x-2^1/2+1). Find the integral. Simplifying. Simplify the expression inside the integral. Divide 9.8284271+x^5+5.4641016x^3 by -0.4142136+x.

Final answer to the problem

$\frac{x^{5}}{5}+\frac{32}{309}x^{4}+\frac{33}{577}x^{3}+\frac{7}{197}x^2+\frac{33}{1121}x+9.8406204\ln\left(x-0.4142136\right)+C_0$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of ((x^5+(23^0.5+2)x^3)/(x+-12^0.5))dx using partial fractionsSolve integral of ((x^5+(23^0.5+2)x^3)/(x+-12^0.5))dx using basic integralsSolve integral of ((x^5+(23^0.5+2)x^3)/(x+-12^0.5))dx using u-substitutionSolve integral of ((x^5+(23^0.5+2)x^3)/(x+-12^0.5))dx using integration by partsSolve integral of ((x^5+(23^0.5+2)x^3)/(x+-12^0.5))dx using trigonometric substitution

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Function Plot

Plotting: $\frac{x^{5}}{5}+\frac{32}{309}x^{4}+\frac{33}{577}x^{3}+\frac{7}{197}x^2+\frac{33}{1121}x+9.8406204\ln\left(x-0.4142136\right)+C_0$

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5
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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
D□x
∫
∫◻
|◻|
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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$\int x^2\cos\left(2x\right)dx$

Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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