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Find the integral $\int\frac{5x^2+3}{x^2\left(x^2+2\right)}dx$

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Solution

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Final Answer

$\frac{-3}{2x}+\frac{7\sqrt{2}}{4}\arctan\left(0.707106x\right)+C_0$
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Step-by-step Solution

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Rewrite the fraction $\frac{5x^2+3}{x^2\left(x^2+2\right)}$ in $3$ simpler fractions using partial fraction decomposition

$\frac{5x^2+3}{x^2\left(x^2+2\right)}=\frac{A}{x^2}+\frac{Bx+C}{x^2+2}+\frac{D}{x}$

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$\frac{5x^2+3}{x^2\left(x^2+2\right)}=\frac{A}{x^2}+\frac{Bx+C}{x^2+2}+\frac{D}{x}$

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Learn how to solve classify algebraic expressions problems step by step online. Find the integral int((5x^2+3)/(x^2(x^2+2)))dx. Rewrite the fraction \frac{5x^2+3}{x^2\left(x^2+2\right)} in 3 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C, D. The first step is to multiply both sides of the equation from the previous step by x^2\left(x^2+2\right). Multiplying polynomials. Simplifying.

Final Answer

$\frac{-3}{2x}+\frac{7\sqrt{2}}{4}\arctan\left(0.707106x\right)+C_0$

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

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Plotting: $\frac{-3}{2x}+\frac{7\sqrt{2}}{4}\arctan\left(0.707106x\right)+C_0$

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a
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d
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n
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x
y
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(◻)
+
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×
◻/◻
/
÷
◻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: Classify algebraic expressions

An algebraic expression can be classified as a monomial, binomial, trinomial or polynomial, depending on the number of terms.

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