yr2 chap 11 integration

• if a problem contains sin^2x, cos^2x or tan^2x, use trig identities to rearrange it into an easier form
• if you have a product of two expressions which do not relate to each other, use integration by parts
• if you have a fraction with multiple factors on the bottom, split it into partial fractions first then use the fact that ln x differentiates to 1/x to integrate the result
• if you get a question in the form $\lim \delta x \rightarrow 0\:\:\:\:\sum^b_{x=a} f(x)\: \:\delta x$, this is a lot easier than it looks, it just means integrate f(x) with an upper limit of b and lower limit of a
• if a problem is either a product of a function and its derivative, or a quotient of a function and its derivative, use the reverse chain rule
• to use reverse chain rule with a quotient, try setting y to equal ln of the denominator and differentiating y, then adjust the multiple to make it equal to the numerator
• to use reverse chain rule with a product, try setting y to equal the function without the derivative and differentiate y, then adjust the multiplke to make it equal to the original