Qual è l'integrale di tan ^ 5 (x) dx tan5(x)dx?
Risposta:
int tan^5 x dx=1/4tan^4 x -1/2*tan^2 x+ln sec x+C∫tan5xdx=14tan4x−12⋅tan2x+lnsecx+C
Spiegazione:
Il dato è da trovare int tan^5 x dx∫tan5xdx
Soluzione:
int tan^5 x* dx∫tan5x⋅dx
int tan^5 x* dx=int tan^3 x*tan^2 x dx∫tan5x⋅dx=∫tan3x⋅tan2xdx
int tan^5 x *dx=int tan^3 x*(sec^2 x-1) dx=int (tan^3 x sec^2 x-tan^3 x) dx∫tan5x⋅dx=∫tan3x⋅(sec2x−1)dx=∫(tan3xsec2x−tan3x)dx
int tan^5 x* dx=int (tan^3 x sec^2 x)dx-int tan^3 x dx∫tan5x⋅dx=∫(tan3xsec2x)dx−∫tan3xdx
int tan^5 x* dx=int (tan^3 x sec^2 x)dx-int tan^2 x *tan x dx∫tan5x⋅dx=∫(tan3xsec2x)dx−∫tan2x⋅tanxdx
int tan^5 x* dx=int (tan^3 x sec^2 x)dx-int (sec^2 x-1) *tan x dx∫tan5x⋅dx=∫(tan3xsec2x)dx−∫(sec2x−1)⋅tanxdx
int tan^5 x *dx=∫tan5x⋅dx=
int (tan^3 x sec^2 x)dx-int (tan x*sec^2 x)dx+int (tan x) dx∫(tan3xsec2x)dx−∫(tanx⋅sec2x)dx+∫(tanx)dx
int tan^5 x *dx=1/4tan^4 x -1/2*tan^2 x+ln sec x+C∫tan5x⋅dx=14tan4x−12⋅tan2x+lnsecx+C
Dio benedica .... Spero che la spiegazione sia utile.