Integration by substitution KUS objectives BAT Integrate using

Integration by substitution • KUS objectives BAT Integrate using a substitution BAT find a definite integral using a substitution, including converting the bounds Starter:

Integration by Substitution This method follows from And takes things further so we can attempt functions we could not Integrate before now

WORKING OUT So by inspection

WORKING OUT Substitution So by substitution To integrate this, you need to replace the x terms with equivalent u terms, and replace the dx with an equivalent du

Consider the power on the bracket. As it is a power 3, it must have been a power 4 before differentiation WORKING OUT Chain rule So by inspection

WORKING OUT Substitution So by substitution To integrate this, you need to replace the x terms with equivalent u terms, and replace the dx with an equivalent du

Start by trying y = ln |denominator| WORKING OUT Chain rule So by inspection

WORKING OUT Substitution So by substitution

WORKING OUT Substitution

WORKING OUT Substitution Does not simplify !

WORKING OUT Substitution

• KUS objectives BAT Integrate using a substitution BAT find a definite integral using a substitution, including converting the bounds self-assess One thing learned is – One thing to improve is –

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