Ta có: \(\int\dfrac{xdx}{x^2+3}\)

Đặt \(u=x^2+3\left(u>0\right)\) 

Có \(du=2xdx\)

\(\Rightarrow\int\dfrac{xdx}{x^2+3}=\)\(\int\dfrac{du}{2u}=\dfrac{1}{2}ln\left(u\right)=\dfrac{1}{2}ln\left(x^2+3\right)\)

Ta có: \(F\left(x\right)=\dfrac{1}{x}=\int x^2f\left(x\right)dx\)
Hay \(F'\left(x\right)=-\dfrac{1}{x^2}=x^2f\left(x\right)\Rightarrow f\left(x\right)=\dfrac{-1}{x^4}\)

Có: \(f'\left(x\right)=\dfrac{4}{x^3}\) \(\Rightarrow I=\int f'\left(x\right)x^3lnxdx=\int\dfrac{4}{x^3}x^3lnxdx=4\int lnxdx\)

Đặt: \(\left\{{}\begin{matrix}u=lnx\\dv=dx\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}du=\dfrac{1}{x}dx\\v=x\end{matrix}\right.\)

\(\Rightarrow I=\text{4}(xlnx-\int x\dfrac{1}{x}dx)=4x\left(lnx-1\right)\)

uses crt;

var t,n,m:longint;

//chuongtrinhcon

function gt(k:longint):longint;

var i,a:integer;

begin

a:=1;

for i:=1 to k do 

  a:=a*i;

gt:=a;

end;

//chuongtrinhchinh

begin

clrscr;

readln(n,m);

writeln(gt(n)+gt(m);

readln;

end.

\(y=cos^2x-cosx=\left(cosx-\dfrac{1}{2}\right)^2-\dfrac{1}{4}\ge-\dfrac{1}{4}\)

\(y=cos^2x-cosx-2+2=\left(cosx+1\right)\left(cosx-2\right)+2\le2\)

\(\Rightarrow-\dfrac{1}{4}\le y\le2\)

\(\Rightarrow\) Có 3 giá trị nguyên \(y=\left\{0;1;2\right\}\)

\(\int xcosx.dx=\int\left(xcosx+sinx\right)dx+\int\left(-sinx\right)dx\) = \(xsinx+cosx+C\)

A = [  ]

for i in range(20):

        A.append(int(input("Nhập phần tử thứ " + str(i+1) + ": ")))

tong = sum(A)

trung_binh = tong / len(A)

print("Mảng A =", A)

print("Giá trị trung bình của mảng A là", trung_binh)