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Integrate x^2/(1+x^2)dx

Unlike if we had just x in the numerature, here the chain rule will do us no good. Integration by parts in this case also is little help - we end up with expressions at least as difficult as we started with....
LH
Answered by Laird H. • Maths tutor
8689 Views

Solve the simultaneous equations: 6a + b = 16 and 5a - 2b = 19

Rearrange the first equation to give b as the subject. b = 16 - 6a Then substitute that equation for b into the second equation. 5a - 2(16 - 6a) = 19 Simplify this equation (remembering to take account of th...
FL
Answered by Francesca L. • Maths tutor
5159 Views

Complete this substitution question: x^​3 - 25 = 103 - x^​3

Firstly, let's move the x^​3's onto the same side (and preferably keep them positive). Let's add x^​3 to both sides, which means the RHS will now read '2x^​3 - 25' and the LHS will read '103'. Next we want t...
AJ
Answered by Aoife J. • Maths tutor
3485 Views

Find, w.r.t to x, both the derivative and integral of y=6*sqrt(x)

Understand the question: 'w.r.t' stand for 'with respect to', so the qestions is asking for the dericative and integral to be calcuated in terms of x - so find dy/dx and (integral sign) y dx. Sqrt(x) is the ...
JR
Answered by Jake R. • Maths tutor
5399 Views

Solve the differential equation: (dy/dx) = 6xy^2

Start by recognising that this is a separable differential equation; it can be written with all of the x's on one side of the equals sign, and all of the y's on the other. The first step is to rearrange so t...
MJ
Answered by Michael J. • Maths tutor
10863 Views