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Evaluate the integral \int \frac{x}{x tan(x) + 1} dx using integration by substitution, hence evaluate \int \frac{x}{x cot(x) - 1} dx.

(STEP I 2017, Q1i)For the first part, the hint u = x sin(x) + cos(x) is given. It can be seen that this is the denominator once the fraction is multiplied by cos(x) / cos(x). The answer is ln(x sin(x) + c...

Answered by Shreyas V. • STEP tutor

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To what extent was Mary Queen of Scots reign defined by her marriages?

(This is a brief plan for how I would answer this essay question)Intro: The main things that define Mary Queen of Scots reign was her marriages, her religion and with her relationship with Elizabeth I and...

Answered by Victoria H. • History tutor

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In the age of modern healthcare, every time a patient dies after a routine operation or procedure, it’s a case of medical error.

This is a partial response for you to read and get a feel for the type of response examiners are looking for. This extract is around a 4A in the BMAT mark scheme. With today's surg...

Answered by Harry C. • BMAT (BioMedical Admissions) tutor

7692 Views

Why does sum(1/n) diverge but sum(1/n^2) converge?

Sum(1/n) is shown to converge by bracketing the series correctly and then comparing it with a series we know diverges. Sum(1/n^2) can be shown to converge via the integral test (using y=1/x^2), where the...

Answered by • MAT tutor

15749 Views

Show that if a^n - 1 is prime then a = 2. If n is not prime, can 2^n-1 be prime?

This question is based on MAT 2015 question 2. This question has already built up the generalized difference of two powers in the buildup. We can apply this to aⁿ - 1 to give: aⁿ- 1...

Answered by Mark W. • MAT tutor

1636 Views