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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

PP
Answered by Pawel P. • Maths tutor
3715 Views

How would I differentiate y=2(e^x)sin(5x) ?

We can see that we have the product of two different functions, and so we need to use the product rule. We will separate the function and label each part u and v for clarity. So we let u = 2ex ...

SP
Answered by Scott P. • Maths tutor
4622 Views

theta = arctan(5x/2). Using implicit differentiation, find d theta/dx.

First, we must rearrange to give 2tan(θ) = 5x. Differentiate both sides with respect to x: 2sec2(θ)dθ/dx = 5 Use identity sin2(θ) + cos2(θ) = 1, dividing through by cos

CW
Answered by Callum W. • Maths tutor
4220 Views

Bob sprints down a 100 metre track as fast as he can and as he arrives at the finish, a light gate cuts a timer that has been active since Bob began his sprint. It reads 12.45 seconds. calculate Bobs average speed during the sprint.

s=distance/time = 100/12.45 =8.03m/s

RW
Answered by Richard W. • Maths tutor
2694 Views

f(x) = x^3 + 3x^2 + 5. Find f'(x) and f''(x).

With differentitaion you multiply the fatcor it's raised by and minus one from the order

e.g. y = x^n so y' = nx^(n-1)

So f'(x) = 3x^2 + 6x and f''(x) = 6x + 6

NS
Answered by Nikita S. • Maths tutor
9322 Views

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