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How do you do integration by parts?

Split the equation into two : one that you are going to integrate, and the other one you want to differentiate. then, apply formula uv - integral(v * du)

Answered by Harvin I. • Maths tutor

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A curve C has equation y=(2x-3)^5. Find the equation of the normal of this curve at point P with y coordinate -32.

Finding normals and tangents to curves is a very common question in A-level maths papers, especially core 3 modules, giving between 5-8 marks depending on complexity. In order to start this question, the ...

Answered by Natalie C. • Maths tutor

10501 Views

How do you differentiate (2x+xe^6x)/(9x-(2x^2)-ln(x)) w.r.t. x?

This problem requires using the quotient rule, product rule and the chain rule. The derivative of the entire thing is ((du/dx)v-(dv/dx)u)/v^2 where u=2x+xe^6x and v=9x-2x^2-lnx. dv/dx is relatively strait...

Answered by Seth H. • Maths tutor

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The equation of a curve is x(y^2)=x^2 +1 . Using the differential, find the coordinates of the stationary point of the curve.

Firstly we need to use product rule to find the dy/dx of the left hand side (LHS). Using implicit differentiation, we know the differential of y^2 is 2y(dy/dx). Then use to product rule to obtain the dy/d...

Answered by Grace C. • Maths tutor

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