Integrate the function f(x) = 1/(4x-1)

t Using the fact that d/dx ( ln g(x)) = g'(x)/g(x), we can see that the integral of this function will be an ln function. From observing f(x) we see that if the answer was ln(4x-1) then f(x) would need to be 4/(4x-1). This is four times bigger than what we want. To obtain the correct integral, we simply multiply ln(4x-1) by 1/4 to get rid of the 4 in the numerator, and so we arrive at the final answer of 1/4 ln(4x-1)

SV

Related Maths A Level answers

All answers ▸

(a) Express (1+4*sqrt(7))/(5+2*sqrt(7)) in the form a+b*sqrt(7), where a and b are integers. (b) Then solve the equation x*(9*sqrt(5)-2*sqrt(45))=sqrt(80).


Identify the stationary points of f(x)=3x^3+2x^2+4 (by finding the first and second derivative) and determine their nature.


A radio sells for £63, after a 40% increase in the cost price. Find the cost price.


f (x) = (x^2 + 4)(x^2 + 8x + 25). Find the roots of f (x) = 0