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How do you find the integral of (2+5x)e^3x ?

If we were to expand the brackets for this question we might be able to get to an answer however there is a much simpler way of solving the problem. As this question is made up of two expressions of x multip...
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Answered by Olivia C. • Maths tutor
6338 Views

If a particle of mass m is launched vertically upwards from the ground with velocity u m/s, how long will it take to return to the ground in terms of m, u and g?

Taking upwards to be positive, and using the 'suvat' equation s=ut+1/2at 2 we know that u=u, a=-g and s=0 when the particle returns to the ground. Then we solve for t: 0=ut-1/2gt 2 0=t(u-1/2gt) So the partic...
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Answered by Jackie V. • Maths tutor
3602 Views

Use the substitution u=x^2-2 to find the integral of (6x^3+4x)/sqrt( x^2-2)

First use the substitution to find du/dx which is 2x. From this we now know that dx= du/2x (just re-arranging.) Substituting that into the integral we now get (6x 3 +4x)/ (sqrt (u) x 2x) du. Cancelling out t...
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Answered by Khalil S. • Maths tutor
10671 Views

Let f(x)=x^3 - 2x^2 + 5. For which value(s) of x does f(x)=5?

Although it can be tempting to dive straight into such a question, its always useful in mathematics to take a step back and assess the question before scribbling down panicked answers. For instance, in this ...
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Answered by Jed G. • Maths tutor
4174 Views

Integrate lnx

This question often throws maths students off fairly easily as they are generally not taught the integral of lnx, and do not usually realise that integration by parts can be used for anything, as you can use...
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Answered by Owen M. • Maths tutor
3822 Views