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integration by parts: x^-2lnx

u=lnx du/dx = 1/x dv/dx=x^-2 v= -1/x =uv - (integral of)vdu/dx (-lnx)/x + integral of x^-2 =(-lnx)/x - 1/x +c
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Answered by Fraser S. • Maths tutor
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Split 1/x^2-1 into partial fractions

First we need to factorise the denominator into (x-1)(x+1). Now we identify that 1/(x-1)(x+1) is equivalent to A/(x-1) + B/(x+1) and now we solve to find the values of A and B. By simplifying the equivalent ...
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Answered by Thomas M. • Maths tutor
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Solve for x: logx(25) = log5(x)

logx(25) = log5(x)2logx(5) = log5(x)2/log5(x) = log5(x)2 = (log5(x))^2sqrt(2) = log5(x)x = 5^sqrt(2)
Answered by • Maths tutor
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Simplify 5p + 2q – 3p – 3q

Firstly, look at the number in front of the letter 'p'. This is 5p and -3p. By ignoring the 'p', as they both have it, do 5-3 which is 2 and so that part of the answer will be 2p. Then look at the letter 'q'...
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Answered by Radhika A. • Maths tutor
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Matthew gets £100 for his 16th birthday and chooses to invest the money into a bank with a 2% annual interest rate. By which birthday will Matthew have more than £150 in his account?

This a geometric sequence with first term 'a' as 100 and common ratio 'r' of 1.02. 100 x 1.02 n > 150 1.02 n > 150/100 =1.02 n > 1.5 log 10 (1.02 n ) > log 10 (1.5) Using power rule, n[log 10 (1....
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