Question 1

For \(x > 0\), compute \(\int \frac{\ln(x)}{x^2} dx\).

# install.packages(c("ggformula","mosaicCalc"))
library(ggformula)
## Warning: package 'ggformula' was built under R version 4.5.2
## Loading required package: ggplot2
## Loading required package: scales
## Loading required package: ggiraph
## Warning: package 'ggiraph' was built under R version 4.5.2
## Loading required package: ggridges
## Warning: package 'ggridges' was built under R version 4.5.2
## 
## New to ggformula?  Try the tutorials: 
##  learnr::run_tutorial("introduction", package = "ggformula")
##  learnr::run_tutorial("refining", package = "ggformula")
library(mosaicCalc)
## Warning: package 'mosaicCalc' was built under R version 4.5.2
## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2
## 
## Attaching package: 'mosaicCalc'
## The following object is masked from 'package:stats':
## 
##     D
f <- makeFun(log(x) / x^2 ~ x)
anti_f <- antiD(f(x) ~ x)
anti_f
## function (x, C = 0) 
## {
##     F <- makeF(log(x)/x^2)
##     evalFun(F, x = x, .const = C)
## }
## <environment: 0x000002460a672ea8>

Question 2

Compute \(\int \frac{8x}{(1 - x^2)^4} dx\).

# install.packages(c("ggformula","mosaicCalc"))
library(ggformula)
library(mosaicCalc)
g <- makeFun((8 * x) / ((1 - x^2)^4) ~ x)
anti_g <- antiD(g(x) ~ x)
anti_g
## function (x, C = 0) 
## {
##     F <- makeF((8 * x)/((1 - x^2)^4))
##     evalFun(F, x = x, .const = C)
## }
## <environment: 0x0000024600b1faf0>

Question 3

Write the number 201 in words.

# install.packages("english")
library(english)
## Warning: package 'english' was built under R version 4.5.2
## 
## Attaching package: 'english'
## The following object is masked from 'package:scales':
## 
##     ordinal
words(201)
## [1] "two hundred one"

Question 4

Convert \(5 \pi\) radians into degrees.

# install.packages("pracma")
library(pracma)
## 
## Attaching package: 'pracma'
## The following objects are masked from 'package:Matrix':
## 
##     expm, lu, tril, triu
value <- rad2deg(rad = 5 * pi)
cat("5 pi radians =",value,"degrees","\n")
## 5 pi radians = 900 degrees