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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
5598 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
6309 Views

Why do skeletal formulae not show the hydrogens bonded to carbons but do on other elements?

Because carbon atoms have 4 electrons in their outer shell so always form 4 covalent bonds in a molecule, so the number of hydrogen atoms bonded can be inferred by subtracting however many bonds the carbon i...
MA
Answered by Megan A. • Chemistry tutor
2943 Views

Why do I have to study maths?

Maths is very important in real life. You use it day to day from basic addition and subtraction to working out percentage discounts in shops. Some of the more complex maths like algebra is used in fields lik...
JP
Answered by Jack P. • Maths tutor
3380 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
4614 Views