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you need to think about how the integral will be simpliefied, basically you are trying to get to a state where only one function of x resides in the integral. so if you have an x² sin3x dx insi...

y′=3x2 −6x

use of y′ = 0

0= 3x^2 - 6x

0= 3x(x-2)

therefore either x=0 or x=2

when x=0 y=1, when x=2 y=-3

(0, 1) or (2, −3) 

y''=6x-6

when x=0 y''=6(...

Start with the LHS:

(cos^4x - sin^4x) / cos^2x 

Recognise the difference of two squares on the top line, which simplifies to (cos^2x - sin^2x)(cos^2x + sin^2x):

(cos^2x - sin^2x)(cos^...

Say you have two functions, A and B, and A is the gradient of B. That is to say, A is as high as B is steep (at any point). Equally, A is as high as the rate of change of B (at any point). Now let’s say w...

integral of cos²(x)*sin(x) we notice that we can use the spot the ball method here: Guessed integral: cos³(x) Differentiated Guessed Integral: -3sin(x)cos²(x), therefore o...