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Integrate 2x/(x^2+3) using the substitution u=x^2+3

u=x² + 3

du/dx=2x

dx=du/2x

2x/(x²+3) dx becomes (2x/u) * (du/2x)

the 2x terms cancel out giving 1/u du

this integrates to ln(u)+c becoming ln(x

Answered by Tom S. • Maths tutor

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If timber prices fall by 30%, what will be the expected % change in demand for timber in the economy if the Price Elasticity of Demand is -0.5, and explain the effect on revenue for a timber-selling firm.

Price Elasticity of Demand (PED) is a measure of the responsiveness of demand to a change in price. A PED of -0.5 suggests demand is price inelastic – as Price falls by 1%, Demand will increase by 0.5% (l...

Answered by Harry C. • Economics tutor

1715 Views

Core 1: Given that y = x^4 + x^2+3. Find dy/dx

First what we need to do is we need to think of what the question is asking us to find. In this case it is dy/dx but what is this. This is the rate of change of y with respect to x. For understanding pur...

Answered by David S. • Maths tutor

2842 Views

Write x^2 + 8x + 7 in the form (x + a)^2 + b

We work from right to left (x + a)² = x² + 2ax + a² 2a = 8 [coefficients of x must match] a = 4 (x + 4)² = x² + 8x + 16 [substitute in a = 4] x^2...

Answered by Will M. • Maths tutor

12731 Views

How do I do definite integrals?

A definite integral is an indefinite integral with set limits. If we consider integration as a way of calculating the area under a curve, a definite integral calculates the area under the curve between tw...

Answered by Charlie J. • Maths tutor

3042 Views