Further Integration

Integration by Parts

Integration by parts twice

Integration of e^ax.cos(bx) (integration by parts twice)

Integration by parts (explained)

Integration of e^x.cos(x) by parts twice (infinite loop?)

Integration of e^x.cos(x) by parts twice (infinite loop?)

Integration by Substitution

Integration by substitution

Integration by substitution

Integration by substitution

Definite integral using substitution

Definite integral using substitution

Integration by Substitution, Trig Identity

Integration by substitution, trig identity

Differential Equations

Differential equation, separation of variables and partial fractions

Particular solution to differential equation with 1/cos^2x

Differential equation involving separation of variables

Finding general solution for a separable differential equation

First order linear ODE using integration factor example

Particular solution for a differential equation

Solving a first order linear ODE using integration factor method

Second order linear non-homogenous ODE with repeated (equal) roots

Second order linear non-homogenous ODE

Trigonometric Integrals

Definite integral involving tan^2

Solving a trigonometric integration equation

Trigonometric integration: sin^2 x

Trigonometric integration: cot^2 2x

Trigonometric integration: sin(x).cos(x)

Trigonometric integration: sin(x)/cos^2(x)

Trigonometric integration: (1+sin x)^2

Integration of cos^4 using trig identity

Modulus Integration

Integrating with modulus x

Exponential Integrals

Piecewise integration with exponential functions

Integral of exponential

Integration using Trig Substitution

Integrating 1/(x^2 + a^2) using trig substitution

Integration with irreducible quadratic in denominator using trig substitution

Integration using trigonometric substitution x=sin(u)

Integration of Logarithms

Integral of ln(x) using integration by parts

Integral of ln^2 (x) using substitution and IBP twice

Integration by parts: sqrt(x).ln(x)

Parametric Area

Area under a parametric curve (Edexcel Pure Maths 2 paper 2 Oct 2020 Q12)

Finding Function from Integral

Particular solution f(x) from f’(x) and a given point (reverse chain rule)

Standard Integrals

Definite integral of 2/(4x+5)

Integral of 2/(3x+1)

Integration using Partial Fractions

Definite integral using partial fractions

Integration by Subst & Parts

Integration by substitution AND by parts

Integration by substitution AND by parts

Basic Trig Integral

Integration of sin

Differential Equations

Differential equation, separation of variables and partial fractions

Particular solution to differential equation with 1/cos^2x

Differential equation involving separation of variables

Finding general solution for a separable differential equation

First order linear ODE using integration factor example

Particular solution for a differential equation

Particular solution to separable differential equation

Solving a first order linear ODE using integration factor method

Second order linear non-homogenous ODE with repeated (equal) roots

Second order linear non-homogenous ODE

Differential Equations

Differential equation, separation of variables and partial fractions

Particular solution to differential equation with 1/cos^2x

Differential equation involving separation of variables

Finding general solution for a separable differential equation

First order linear ODE using integration factor example

Particular solution for a differential equation

Particular solution to separable differential equation

Solving a first order linear ODE using integration factor method

Second order linear non-homogenous ODE with repeated (equal) roots

Second order linear non-homogenous ODE

Exponential Integrals

Piecewise integration with exponential functions

Integral of exponential