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How do you integrate ln(x)?

Here, we use integration by parts. We must imagine ln(x) as a product of 1 and ln(x). We usually take the function of x to be our dv/dx, however, in the case of ln(x), we take that to be u (it is a special c...
OD
Answered by Omkar D. • Maths tutor
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Lottie has a bag of applies. She gives half of them to Fred. Fred eats two and then has four left. How many apples did Lottie have at the start?

General method 1. Write the information down in equation form defining unique symbols to represent the unknowns2. DOF analysis: Count the number of equations and unknowns? a. If #E = #U → unique solution b. ...
NG
Answered by Niraj G. • Maths tutor
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Find the constant term in the expression (x^2-1/x)^9

This problem uses the binomial expansion formula: (x+y) n = k=0 Z n n C k x k y n-k .But lets try to understand where this formula comes from by doing the problem without it to start of with.We have the expr...
VY
Answered by Vincent Y. • Maths tutor
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Express 12.5% as a fraction.

To make a percentage into a fraction you divide it by 100. This means 12.5% is 12.5/100. However, when giving fractions as an answer it needs to be done in the simplest form. To do this you need to find the ...
TG
Answered by Thanu G. • Maths tutor
112449 Views

Differentiate: tan(2x) cos(x)

Explain the product rule : d/dx ( f(x) . g(x) ) = f'(x).g(x) = g'(x) . f (x) 2. Briefly run through trigonometric derivatives .* cos (x) differentiates to: -sin(x)* tan (x) differentiates to: sec^2 (x) 3. Br...
SD
Answered by Shreyasi D. • Maths tutor
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