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

u=x 2 + 3 du/dx=2x dx=du/2x 2x/(x 2 +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 2 +3)+c
TS
Answered by Tom S. • Maths tutor
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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 purpose...
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Answered by David S. • Maths tutor
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Write x^2 + 8x + 7 in the form (x + a)^2 + b

We work from right to left (x + a) 2 = x 2 + 2ax + a 2 2a = 8 [coefficients of x must match] a = 4 (x + 4) 2 = x 2 + 8x + 16 [substitute in a = 4] x 2 + 8x + 16 + b = x 2 + 8x + 7 [equate sides and solve for...
WM
Answered by Will M. • Maths tutor
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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 two p...
CJ
Answered by Charlie J. • Maths tutor
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A Curve has parametric equation x=2sin(t), y= 1+cos(2t), -pi/2<=t<=pi/2. a) Find dy/dx when t=pi/3. b) Find the Cartesian equation for the curve in form y=f(x), -k<=x<=k. c) Find the range of f(x)

x=2sin(t), y=1+cos(2t) a) By chain rule, dy/dx = (dy/dt)/(dx/dt) dy/dt = -2sin(2t), dx/dt= 2cos(t) dy/dx= -sin(2t)/cos(t) dy/dx=-2sin(t)cos(t)/cos(t) dy/dx=-2sin(t) when t = pi/3, dy/dx= -sqrt(3) b) dy/dx = ...
MB
Answered by Max B. • Maths tutor
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