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Find the integral of the function y = ln(x)

(I can use the whiteboard for to explain it better)1) Express y = ln(x) as y = ln(x) * 12) Use integration by parts with u = ln(x), v'=(1), u'=1/x, v = xintegral = xln(x) - integral(x*1/x) =xln(x) - integral...
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Answered by Anton N. • Maths tutor
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integrate 5x + 3(square root of x)

5/2 x^2 + 2x^3/2 +c
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Answered by Ariana W. • Maths tutor
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Differentiate f(x) = 14*(x^2)*(e^(x^2))

Differentiate f(x) = 14x 2 e x^2 To approach this problem we first need to realise that f(x) is made up of two simpler functions multiplied together. This tells us that we should use the product rule to solv...
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Answered by Toby C. • Maths tutor
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If I have a ball thrown horizontally with a speed u off a building of height h , how do I calculate its speed when it hits the ground?

Here we will want to use the SUVAT equations, which I'm sure you will have come across. Notice that in the question we only have an initial horizontal velocity and because we model all objects as points, we ...
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Answered by Charlotte G. • Maths tutor
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Find the stationary point(s) on the curve 2xsin(x)

Derivative of 2xsin(x): 2sin(x)+2xcos(x)Set derivative equal to zero: 2sin(x)+2xcos(x)=0Solve: only valid when x=0Therefore the only stationary point is (0,0) ie the origin.
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Answered by Seyi O. • Maths tutor
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