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Maths
A Level

How to Integrate ln(x)?

Integrating this expression is a simple trick. We use integration by parts. For this we need a function we can integrate and a function we can differentiate. We know how to differentiate ln(x) which is 1/...

Answered by Jordan R. Maths tutor
5834 Views

Prove the trigonometric identity tan^2(x)+1=sec^2(x)

 We can start with the identity sin2(x)+cos2(x)=1 If we divide through the equation by cos2(x), we get: sin2(x)/cos2(x) + cos2(x)/cos...

Answered by Charlotte W. Maths tutor
14132 Views

Find the equation of the tangent to the curve y = 2x^2 + x - 1 at the point where x = 1.

To get the required tangent equation we need its gradient and the coordinates of a point it passes through. We can then substitute it into the formula y - y1 = m(x - x1). 1. ...

Answered by Beth T. Maths tutor
10195 Views

When do you know to use integration by parts?

You use integration by parts if there's more than one function of x. For example; to integrate xsin(x) you'd use integration by parts as this is two functions of x. The formula to remember is I(udv) =...

Answered by Natasha L. Maths tutor
3487 Views

Compute the indefinite integral of x^8 ln(3x)dx

Using integration by parts, by substituting ln(3x) as u and x^8 as dv/dx, use the formula to plug in the values and complete the calculation to get (x^9)(ln(3x)-1/9)/9

Answered by Pawel P. Maths tutor
3343 Views

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