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Find the integral of $\frac{4x^4+1\cdot -3x^3-18x^2+15x-3}{x^2-5}$

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Final Answer

$\frac{4}{3}x^{3}-\frac{3}{2}x^2+2x+\frac{7}{2\sqrt{5}}\ln\left(x-\sqrt{5}\right)-\frac{7}{2\sqrt{5}}\ln\left(x+\sqrt{5}\right)+C_0$
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Step-by-step Solution

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Find the integral

$\int\frac{4x^4+1\cdot -3x^3-18x^2+15x-3}{x^2-5}dx$

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$\int\frac{4x^4+1\cdot -3x^3-18x^2+15x-3}{x^2-5}dx$

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Learn how to solve integral calculus problems step by step online. Find the integral of (4x^4+1*-3x^3-18x^215x+-3)/(x^2-5). Find the integral. Simplifying. Divide 4x^4-3x^3-18x^2+15x-3 by x^2-5. Resulting polynomial.

Final Answer

$\frac{4}{3}x^{3}-\frac{3}{2}x^2+2x+\frac{7}{2\sqrt{5}}\ln\left(x-\sqrt{5}\right)-\frac{7}{2\sqrt{5}}\ln\left(x+\sqrt{5}\right)+C_0$

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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 ((4x^4+1-3)/(x^2-5))dx using partial fractionsSolve integral of ((4x^4+1-3)/(x^2-5))dx using basic integralsSolve integral of ((4x^4+1-3)/(x^2-5))dx using u-substitutionSolve integral of ((4x^4+1-3)/(x^2-5))dx using integration by partsSolve integral of ((4x^4+1-3)/(x^2-5))dx using trigonometric substitution

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Function Plot

Plotting: $\frac{4}{3}x^{3}-\frac{3}{2}x^2+2x+\frac{7}{2\sqrt{5}}\ln\left(x-\sqrt{5}\right)-\frac{7}{2\sqrt{5}}\ln\left(x+\sqrt{5}\right)+C_0$

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0
a
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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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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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