Find the integral $\int\frac{x^3+x^2-5x+15}{\left(x^2+5\right)\left(x^2+2x+3\right)}dx$

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log

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sin

cos

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csc

asin

acos

atan

acot

asec

acsc

sinh

cosh

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atanh

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Pre-Calculus - Graphing rational functions using 5 steps, g(x) = (-3x^2 + x + 12) / (x^2 - 4)

https://www.youtube.com/watch?v=fG2HAWBNVNE

Algebra 2 - Learning to solve rational equations in math class ((x+3)/(x‐2)) + (5/(x^2‐4)) = 1

https://www.youtube.com/watch?v=y8p0Tpn3BcI

Algebra 1 - Solve an equation with a rational term 1/x= 3+ 7/x^2+7x ex 2

https://www.youtube.com/watch?v=OjNDpBeMpxI

Calculus - Take the log of both sides to find the derivative, y = (x(x^2 + 1)^2)/(sqrt(2x^2 - 1))

https://www.youtube.com/watch?v=7aF6Ck6ZRxw

Implicit differentiation | Advanced derivatives | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=mSVrqKZDRF4

Algebra 2 - How to find all the roots of a polynomial by factoring, y = 6x^3 + x^2 - x

https://www.youtube.com/watch?v=Qi20wNdicXQ

 Function Plot

Plotting: $-5\cdot \left(\frac{1}{\sqrt{5}}\right)\arctan\left(\frac{x}{\sqrt{5}}\right)+5\cdot \left(\frac{1}{\sqrt{2}}\right)\arctan\left(\frac{x+1}{\sqrt{2}}\right)+\ln\left(\sqrt{\left(x+1\right)^2+2}\right)+C_1$

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Go!



(◻)

◻/◻

◻²

◻^◻

√◻

√

^◻√◻

^◻√

∞

log

log_◻

lim

d/dx

D^□_x

∫

∫^◻

|◻|

sin

cos

tan

cot

sec

csc

asin

acos

atan

acot

asec

acsc

sinh

cosh

tanh

coth

sech

csch

asinh

acosh

atanh

acoth

asech

acsch

 How to improve your answer:

 Main Topic: Integrals by Partial Fraction Expansion

The partial fraction decomposition or partial fraction expansion of a rational function is the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.

 Used Formulas

See formulas (4)

Find the integral $\int\frac{x^3+x^2-5x+15}{\left(x^2+5\right)\left(x^2+2x+3\right)}dx$

Related Videos

 Solution

 Formulas

 Videos

Pre-Calculus - Graphing rational functions using 5 steps, g(x) = (-3x^2 + x + 12) / (x^2 - 4)

Algebra 2 - Learning to solve rational equations in math class ((x+3)/(x‐2)) + (5/(x^2‐4)) = 1

Algebra 1 - Solve an equation with a rational term 1/x= 3+ 7/x^2+7x ex 2

Calculus - Take the log of both sides to find the derivative, y = (x(x^2 + 1)^2)/(sqrt(2x^2 - 1))

Implicit differentiation | Advanced derivatives | AP Calculus AB | Khan Academy

Algebra 2 - How to find all the roots of a polynomial by factoring, y = 6x^3 + x^2 - x

 Function Plot

Plotting: $-5\cdot \left(\frac{1}{\sqrt{5}}\right)\arctan\left(\frac{x}{\sqrt{5}}\right)+5\cdot \left(\frac{1}{\sqrt{2}}\right)\arctan\left(\frac{x+1}{\sqrt{2}}\right)+\ln\left(\sqrt{\left(x+1\right)^2+2}\right)+C_1$

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Got a different answer? Verify it!

 How to improve your answer:

 Main Topic: Integrals by Partial Fraction Expansion

 Used Formulas

 Related Topics

Find the integral $\int\frac{x^3+x^2-5x+15}{\left(x^2+5\right)\left(x^2+2x+3\right)}dx$

Related Videos

 Solution

 Formulas

 Videos

Pre-Calculus - Graphing rational functions using 5 steps, g(x) = (-3x^2 + x + 12) / (x^2 - 4)

Algebra 2 - Learning to solve rational equations in math class ((x+3)/(x‐2)) + (5/(x^2‐4)) = 1

Algebra 1 - Solve an equation with a rational term 1/x= 3+ 7/x^2+7x ex 2

Calculus - Take the log of both sides to find the derivative, y = (x(x^2 + 1)^2)/(sqrt(2x^2 - 1))

Implicit differentiation | Advanced derivatives | AP Calculus AB | Khan Academy

Algebra 2 - How to find all the roots of a polynomial by factoring, y = 6x^3 + x^2 - x

 Share this solution with your friends!

 Function Plot

Plotting: $-5\cdot \left(\frac{1}{\sqrt{5}}\right)\arctan\left(\frac{x}{\sqrt{5}}\right)+5\cdot \left(\frac{1}{\sqrt{2}}\right)\arctan\left(\frac{x+1}{\sqrt{2}}\right)+\ln\left(\sqrt{\left(x+1\right)^2+2}\right)+C_1$

beta Got a different answer? Verify it!

 How to improve your answer:

Similar Problems Solved

 Main Topic: Integrals by Partial Fraction Expansion

 Used Formulas

 Related Topics

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