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Let f denote an integral sign, I will write the integrand in square brackets. We can use integration by parts to integrate ln(x), the "trick" here is to imagin ln(x) as 1 x ln(x). Integ...

Let f denote an integral sign, I will write the integrand in square brackets. The formula for integration by parts is given by:f [(u)(dv/dx)]dx = uv - f [((du/dx)(v)]dxTo apply ...

First of all we need to find the integral of our function which is f(x). Since we are integrating with respect to x and our values are in the form of x we can use the rule of raising the power for each x ...

First we need to use trigonometric identities to convert the sin^3(x) to a single power. This is because we cannot integrate trigonometric functions that are above the power of 1. We need to use the doubl...

First, we need to work out the length of each 'part' of string. We are told Jake cuts the string into the ratio 4:3:2 , so there are (4+3+2=9) 9 parts in total. To work out how long each part is, we calc...