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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/x. ...
JR
Answered by Jordan R. • Maths tutor
7653 Views

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

We can start with the identity sin 2 (x)+cos 2 (x)=1 If we divide through the equation by cos 2 (x), we get: sin 2 (x)/cos 2 (x) + cos 2 (x)/cos 2 (x) = 1/cos 2 (x) If we look at the left hand side of the eq...
CW
Answered by Charlotte W. • Maths tutor
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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 - y 1 = m(x - x 1 ). 1. Finding the gradient: To find ...
BT
Answered by Beth T. • Maths tutor
12512 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 x sin(x) you'd use integration by parts as this is two functions of x. The formula to remember is I(udv) = uv - ...
NL
Answered by Natasha L. • Maths tutor
4403 Views

Rearrange to make p the subject. C + 5 p = a ( C – p )

C+5p = a (c-p) C+5p = ac-ap 5p+ap=ac-c p(5+a) = c(a-1) p=(c(a-1))/(5+a)
SM
Answered by Santiago M. • Maths tutor
4741 Views