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Find the integral of e^3x/(1+e^x) using the substitution of u=1+e^x

Differentiate U with respect to x to find dx in terms of du and substitute into the integral so that it is in terms of du, then using e^3x = (e^x)^3 and u = 1+e^x subsitute u in for x and simplify the integr...
CF
Answered by Cory F. • Maths tutor
5715 Views

dx/dt = -5x/2, t>=0. Given that x=60 when t=0, solve the differential equation, giving x in terms of t.

dx/dt = -5x/2 to solve this we must firstly separate the variables ∫2/x dx = -∫5 dt t hen we solve the integrals using basic integration formulae 2lnx = -5t+c. When it comes to the exam, many students forget...
KS
Answered by Kulveer S. • Maths tutor
6430 Views

Describe the stylistic features of Partita No. 4 in D, BWV 828: Sarabande and Gigue by Bach which show that this music was composed in the Baroque period.

The stylistic features relating to genre, tonality, harmony, texture, melody and structure show that this work by Bach is from the Baroque period. Firstly, both the Sarabande and Gigue were dances that very ...
AM
Answered by Adam M. • Music tutor
4741 Views

What is natural selection?

Natural selection is one of the fundamental mechanisms of the process of evolution. There are 4 key things to remember about the process of natural selection.1) There is genetic variation within a population...
EE
Answered by Eva E. • Biology tutor
3931 Views

What is the importance of Michelangelo's David?

Michelangelo's David (1501-1504) is one of the worlds most famous sculptures, but the fame and importance of David in Florence is shown not only in Michelangelo's handling of the male nude but also the histo...
RC
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