# What is Substitution: Definition and 815 Discussions

A substitution reaction (also known as single displacement reaction or single substitution reaction) is a chemical reaction during which one functional group in a chemical compound is replaced by another functional group. Substitution reactions are of prime importance in organic chemistry. Substitution reactions in organic chemistry are classified either as electrophilic or nucleophilic depending upon the reagent involved, whether a reactive intermediate involved in the reaction is a carbocation, a carbanion or a free radical, and whether the substrate is aliphatic or aromatic. Detailed understanding of a reaction type helps to predict the product outcome in a reaction. It also is helpful for optimizing a reaction with regard to variables such as temperature and choice of solvent.
A good example of a substitution reaction is halogenation. When chlorine gas (Cl2) is irradiated, some of the molecules are split into two chlorine radicals (Cl•) whose free electrons are strongly nucleophilic. One of them breaks a C–H covalent bond in CH4 and grabs the hydrogen atom to form the electrically neutral HCl. The other radical reforms a covalent bond with the CH3• to form CH3Cl (methyl chloride).

View More On Wikipedia.org
1. ### Use substitution to solve the definite integral

I have ##1-x^2 = 1- \sin^2 θ = \cos^2 θ## and ## dx =cos θ dθ## ##\int_0^{0.5} (1-x^2)^{1.5} dx = \int_0^{\frac{π}{6}} [cos ^2θ]^\frac{3}{2} dθ = \int_0^{\frac{π}{6}} [cos ^4θ] dθ## Suggestions on next step.

7. ### Integration Substitution Techniques for quadratic expressions under square roots

Hi, With respect to the techniques mentioned in point 2 and 3: Can someone explain or even better, post a link for an explanation or a videos showing the use of these two techniques. Below excerpt shows problems 4 and 5 referenced in the above 2 points:
8. ### I Where did this substitution technique go wrong?

We can solve ##y'(x) = (ax+b)y(x)## by rearranging to obtain ##\frac{y'}{y} = ax +b## and solving in terms of an exponential. I tried an alternative technique to see if it would work, and somewhere I went wrong. The point of the technique is that a slightly simpler version of the problem should...
9. ### B Are Both Answers Correct for Trigonometric Substitution Integral?

Last night I tried to calculate from an automatically generated Wolfram Alpha problem set: $$\int{\frac{1}{\sqrt{x^2+4}}}dx$$ I answered $$\ln({\frac{\sqrt{x^2+4}}{2}+\frac{x}{2}})+C$$ The answer sheet gave: $$\ln({\sqrt{x^2+4}+x})+C$$ I couldn't see where I had gone wrong, so I tried...
10. ### I Confusion about the Substitution rule

Given is a function ##P(E)## and its derivative ##f(E)##. Writing ##E## in terms of ##v## according to ##E=\frac{1}{2}mv^2## gives the derivative ##g(v)=f(E)mv## and ##dE=mvdv##. My issue arises from the premise that I learned; Integrals and derivatives are based on steps of a fixed constant...
11. ### Solving this integral with u substitution

Evaluate ##\displaystyle\int_{0}^{3}\frac{x+3}{\sqrt{x^{3}+1}}dx+5## W|A returned 11.7101 ok subst is probably just one way to solve this so ##u=x^{3}+1 \quad du= 3x^2##
12. ### MHB Antidifferentiation by Substitution

1.$\int x^2 e^{x^3} dx$ 2. $\int sin(2x-3)dx$ 3. $\int (\cfrac {3dx}{(x+2)\sqrt {x^2+4x+3}} )$ 4. $\int (\cfrac {x^3}{(x^2 +4)^\cfrac {3}{2}} )dx$
13. ### Integral using substitution x = -u

Is it possible to solve this integral? I think the substitution ##x=-u## does not help at all since it only changes variable ##x## to ##u## without changing the integrand much. Using that substitution: $$\int \frac{6x^2+5}{1+2^x}dx=-\int \frac{6u^2+5}{1+2^{-u}}du$$ Then how to continue? Thanks

.
15. ### Calculus Textbook for Integration using Hyperbolic substitution

Can someone please tell me the book that contain integration using hyperbolic substitution for beginner? I know that hyperbolic functions is taught in Calculus book but most of them is only some identities and inverses of hyperbolic functions.
16. ### I Integration Using Hyperbolic Substitution

Can someone please show me an example of integration using hyperbolic substitution? Thank you
17. ### Show that the Diffusion Eqn after substitution gives the Helmholtz Eqn

Question: Helmholtz as defined in text: My attempt so far

20. ### Simultaneous equations substitution method

I'm really stuck on this one, I was able to get the answer but not by the substitution method. So its the weight as A and B so I get A + B = 24 A(3) = B(5) so in my head I calculate a few pairs, 3 x 5 = 15 but 3 + 5 only = 8 so the next pair would be 10 and 6 which is still to small so I move...
21. ### Circuit Theory - about the applicability of the substitution theorem

Hi, I've a doubt about the applicability of the substitution theorem in circuit theory. Consider the following picture (sorry for the Italian inside it :frown: ) As far I can understand the substitution theorem can be applied to a given one-port element attached to a port (a port consists of...

27. ### Understanding Integration by Substitution

Not sure how do I start from here, but do I let $$u = lnx$$ and substitute? Cheers
28. ### MHB 2.6.62 inverse integrals with substitution

ok this is from my overleaf doc so too many custorm macros to just paste in code but I think its ok,,, not sure about all details. appreciate comments... I got ? somewhat on b and x and u being used in the right places

48. ### MHB How can substitution make solving integrals easier?

Hi, I've got this problem that I've been trying to work out. I think most of my problems come from the fact that I am not yet well versed in u substitution when it comes to integrals. I'm also not 100% sure what the problem is asking. I've tried doing a couple of things, but they don't seem to...
49. ### A query in integration using method of substitution

Homework Statement :[/B] I was learning the use of standard forms in method of substitution in solving integration. My book has given this method for solving integrals of the type ##\int \frac{lx +m}{ax^2+bx+c} dx##: As an example, the book gives this one: Homework Equations :[/B] The...
50. ### Solving a differential equation with substitution

This is a small part of a question from the book, so I think the format does not really apply here. When doing questions for solving differential equation with substitution, I encountered a substitution ## y(x)=\frac{1}{v(x)} ##. And I am not sure about the calculus in finding ## \frac{dy}{dx}...