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Doing integration with partial fractions

Integral Calculus: Master Advanced Integration Techniques

Integrals

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Antiderivatives

Derivatives and Antiderivatives

Derivative and Antiderivative of a Function

Riemann sum

Riemann Sum

Evaluating integrals with a Riemann sum

Evaluating integrals with a Riemann Sum

Riemann Sum with Trapezoid Approximation

Trapezoidal Approximation of Riemann Sums

Fundamental theorem of calculus

Fundamental Theorem of Calculus Part II

Fundamental Theorem of Calculus Part I

Fundamental Theorem of Calculus

Definite integral

Definite Integral

Integration Techniques

Numerical integration

Numerical Integration

U-Substitution

U-Substitution: Integrating Radical Functions

Not-So-Obvious U-Substitution

Trigonometric substitution

Trigonometric Substitution

Integration of rational functions by partial fractions

Improper integrals

Improper Integrals

Integration by parts

Integration using trigonometric identities

Integration Applications

Areas between curves

Volumes of solids of revolution - Disc method

Volumes of solid with known cross-sections

Volumes of solids of revolution - Shell method

Volumes of solid of revolution - Shell method

Arc length

Average value of a function

Introduction to differential equations

Order and solutions to differential equations

Separable equations

Separable Equations

Applications to differential equations

Modeling with differential equations

Slope fields

Understanding Slope Fields

Euler's method

Euler's Method

Euler"s Method

Euler"s method

Sequence and Series

Introduction to sequences

Monotonic and bounded sequences

Introduction to infinite series

Convergence and divergence of normal infinite series

Convergence & divergence of geometric series

Divergence of Geometric Series

Convergence & divergence of telescoping series

Divergence of harmonic series

Divergence of Harmonic Series

P Series

Convergence and Divergence of P Series

Alternating series test

Alternating Series Test

Convergence of the Alternating Series Test

Divergence test

Divergence Test

Comparison & limit comparison test

Comparison & Limit Comparison Test

Integral test

Integral Test for Series Convergence

Convergence/Divergence of Integral Test

Ratio test

Ratio Test

Convergence & Divergence of Ratio Test

Root test

Root Test

Root Test for Series Convergence

Convergence & Divergence of Root test

Absolute & conditional convergence

Absolute & Conditional Convergence

Radius and interval of convergence with power series

Radius of Convergence of Logarithmic Function

Radius and Interval of Convergence with Power Series

Radius of Convergence of Tangent Function

Functions expressed as power series

Taylor series and Maclaurin series

Approximating functions with Taylor polynomials and error bounds

Parametric Equations and Polar Coordinates

Defining curves with parametric equations

Tangent and concavity of parametric equations

Area of parametric equations

Arc length and surface area of parametric equations

Arc Length of a Parametric Curve

Polar coordinates

Tangents of polar curves

Area of polar curves

Arc length of polar curves

Integral calculus made easy!
Get better marks in calculus class with our complete Integral Calculus help. Our calculus tutors cover all topics you will see in any typical Integration class that deals with single variable functions.

Keeping with your textbook and class, our Integral calculus video lessons walk you through all topics in integral calculus such as, Antiderivative, Integral of trig functions, Definite integral, Indefinite integral, Integration by substitution, Improper integrals and more. Learn the concepts with our tutorials that show you step-by-step solutions to even the hardest integral calculus questions. Then, reinforce your understanding with tons of integral calculus practice.
All our lessons are taught by experienced calculus teachers. Let&apos;s finish your homework in no time, and ACE that exam.

Integral Calculus

sample

math

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Ex 1.

Ex 2.

Ex 3.

Ex 4.

Case 4: Repeated irreducible quadratic factors in partial fractions

Ex 5.

Decomposing a rational function with three distinct linear factors

Partial fraction decomposition and integration of 18/(x³ - 9x)

Partial fractions with repeated linear factors and equating coefficients

Partial fractions with repeated linear factors and integrating the result

Integrating a rational function with an irreducible quadratic factor

Integrating an improper rational function using long division and partial fractions

In this lesson, we will focus on integrating rational functions which requires the use of partial fraction decomposition. Once the fraction has been split into smaller pieces, then it will be easier to integrate. Just make sure that the question really requires partial fractions before using this method. First, we will take a look at fractions where the <a href='[[glossary.html|{"keyword":"Denominator","term":"Denominator"}]]'>denominator</a> is a product of linear factors with no repeats. Second, we will take a look at the case where the denominator does have linear factors with repeats. Third, we will tackle more advance questions where we have quadratic factors which cannot be factored into linear factors, but has no repeats. Lastly, we will look at the hardest type of partial fractions question, where the denominator has irreducible quadratic factors AND repeats. In the end, we will take a look at questions which involves performing long division before we can use partial fraction decomposition.

Integration of rational functions by partial fractions

What You'll Learn

Decompose rational functions into partial fractions based on denominator factors

Identify and apply the four cases: linear factors, repeated factors, irreducible quadratics, and repeated quadratics

Solve for unknown constants using substitution or equating coefficients

Integrate partial fractions using natural logarithms and inverse tangent formulas

Apply polynomial long division when the degree of the numerator exceeds the denominator

What You'll Practice

Factoring denominators into linear and irreducible quadratic factors

Setting up partial fraction decompositions for each case

Solving systems of equations to find numerator constants

Integrating rational functions with repeated linear factors

Using long division to convert improper fractions before decomposition

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

7 Video lessons

Practice exercises

Skills

Partial Fractions

Rational Functions

Integration

Factoring

Long Division

Natural Logarithm

Inverse Tangent

Polynomial Decomposition