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Find the integral of $\frac{9x^4+\frac{9}{2}x^2+5x+4x^6+\frac{10}{3}x^3}{2x^2+3}$

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Solution

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Final Answer

$\frac{2}{5}x^{5}+\frac{1}{2}x^{3}-\frac{9}{4}x+2.755676\arctan\left(\frac{\sqrt{6}}{3}x\right)-\frac{5}{2}\ln\left(\frac{\sqrt{3}}{\sqrt{2x^2+3}}\right)+C_0$
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Step-by-step Solution

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Find the integral

$\int\frac{9x^4+\frac{9}{2}x^2+5x+4x^6+\frac{10}{3}x^3}{2x^2+3}dx$

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$\int\frac{9x^4+\frac{9}{2}x^2+5x+4x^6+\frac{10}{3}x^3}{2x^2+3}dx$

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Learn how to solve integral calculus problems step by step online. Find the integral of (9x^4+9/2x^25x4x^610/3x^3)/(2x^2+3). Find the integral. Simplifying. Divide 9x^4+\frac{9}{2}x^2+5x+4x^6+\frac{10}{3}x^3 by 2x^2+3. Resulting polynomial.

Final Answer

$\frac{2}{5}x^{5}+\frac{1}{2}x^{3}-\frac{9}{4}x+2.755676\arctan\left(\frac{\sqrt{6}}{3}x\right)-\frac{5}{2}\ln\left(\frac{\sqrt{3}}{\sqrt{2x^2+3}}\right)+C_0$

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 ((9x^4+9/2x^2)/(2x^2+3))dx using partial fractionsSolve integral of ((9x^4+9/2x^2)/(2x^2+3))dx using basic integralsSolve integral of ((9x^4+9/2x^2)/(2x^2+3))dx using u-substitutionSolve integral of ((9x^4+9/2x^2)/(2x^2+3))dx using integration by partsSolve integral of ((9x^4+9/2x^2)/(2x^2+3))dx using trigonometric substitution

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Function Plot

Plotting: $\frac{2}{5}x^{5}+\frac{1}{2}x^{3}-\frac{9}{4}x+2.755676\arctan\left(\frac{\sqrt{6}}{3}x\right)-\frac{5}{2}\ln\left(\frac{\sqrt{3}}{\sqrt{2x^2+3}}\right)+C_0$

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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
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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$\int x^2\sin\left(x\right)dx$

Compute the integral

$\int x^2\cos\left(2x\right)dx$

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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