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How can you integrate ln(x) with respect to x?

We can use substitution for this one. Take y=ln(x) to be equal to y= 1 x ln(x)Set u=ln(x) and dv/dx=1Compute du/dx and v:du/dx=1/x and v=xUse given formula - ∫ udv/dx dx = uv - ∫ vdu/dx dx= xln(x) - ∫ x/x dx...
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Answered by Samuel H. • Maths tutor
3735 Views

What is the pythagoras theorem?

a 2 =b 2 +c 2
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Answered by Anwen F. • Maths tutor
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Differentiate the following with respect to x: e^(10x) + ln(6x+2)

We can differentiate the terms separately: The first term e 10x can be differentiated using the chain rule. Let u = 10xWe can differentiate to get du/dx = 10 Differentiating e u with respect to u gives us d/...
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Answered by Meher L. • Maths tutor
4520 Views

integrate 1/(x^2+4x+13)

The first step is to notice that this is a standard integral in the form of 1/(x^2+a^2). In order to reach this form, we must first complete the square. Then we have 1/(x+2)^2-4+13=1/(x+2)^2+9. We can then u...
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Answered by Jim T. • Maths tutor
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The curve C has equation (4x^2-y^3+3^2x)=0. The point P (0,1) lies on C: what is the value of dy/dx at P?

Use the chain rule to differentiate the original equation: this results in 8x-3y^2*(dy/dx) + 2ln(3) 3^2x=0. This can be rearranged to find dy/dx as a function of y and x: 3y^2 (dy/dx)=8x+2ln(3)*3^2x -> dy...
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Answered by Tutor65063 D. • Maths tutor
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