Integralen av $$$\frac{1003605945944011425233769242881280649744658171441 t}{1000000000000000000000000000000000000000000000000}$$$
Relaterad kalkylator: Kalkylator för bestämda och oegentliga integraler
Din inmatning
Bestäm $$$\int \frac{1003605945944011425233769242881280649744658171441 t}{1000000000000000000000000000000000000000000000000}\, dt.$$$
Lösning
Tillämpa konstantfaktorregeln $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ med $$$c=\frac{1003605945944011425233769242881280649744658171441}{1000000000000000000000000000000000000000000000000}$$$ och $$$f{\left(t \right)} = t$$$:
$${\color{red}{\int{\frac{1003605945944011425233769242881280649744658171441 t}{1000000000000000000000000000000000000000000000000} d t}}} = {\color{red}{\left(\frac{1003605945944011425233769242881280649744658171441 \int{t d t}}{1000000000000000000000000000000000000000000000000}\right)}}$$
Tillämpa potensregeln $$$\int t^{n}\, dt = \frac{t^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ med $$$n=1$$$:
$$\frac{1003605945944011425233769242881280649744658171441 {\color{red}{\int{t d t}}}}{1000000000000000000000000000000000000000000000000}=\frac{1003605945944011425233769242881280649744658171441 {\color{red}{\frac{t^{1 + 1}}{1 + 1}}}}{1000000000000000000000000000000000000000000000000}=\frac{1003605945944011425233769242881280649744658171441 {\color{red}{\left(\frac{t^{2}}{2}\right)}}}{1000000000000000000000000000000000000000000000000}$$
Alltså,
$$\int{\frac{1003605945944011425233769242881280649744658171441 t}{1000000000000000000000000000000000000000000000000} d t} = \frac{1003605945944011425233769242881280649744658171441 t^{2}}{2000000000000000000000000000000000000000000000000}$$
Lägg till integrationskonstanten:
$$\int{\frac{1003605945944011425233769242881280649744658171441 t}{1000000000000000000000000000000000000000000000000} d t} = \frac{1003605945944011425233769242881280649744658171441 t^{2}}{2000000000000000000000000000000000000000000000000}+C$$
Svar
$$$\int \frac{1003605945944011425233769242881280649744658171441 t}{1000000000000000000000000000000000000000000000000}\, dt = \frac{1003605945944011425233769242881280649744658171441 t^{2}}{2000000000000000000000000000000000000000000000000} + C$$$A