Răspuns:
f) Integrala se mai scrie
[tex]\displaystyle\int4x\sin(2x^2+2)dx[/tex]
Se face schimbarea de variabilă
[tex]2x^2+2=t\Rightarrow 4xdx=dt[/tex]
[tex]I(t)=\displaystyle\int\sin tdt=-\cos t+\mathcal{C}[/tex]
[tex]I(x)=-\cos(2x^2+2)+\mathcal{C}[/tex]
g)
[tex]\displaystyle\int\tan x(\tan^2x+1)dx=\int\tan x\cdot\dfrac{1}{\cos^2x}}dx=\int\tan x(\tan x)'dx=\\=\dfrac{\tan^2x}{2}+\mathcal{C}[/tex]
Explicație pas cu pas:
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Răspuns:
f) Integrala se mai scrie
[tex]\displaystyle\int4x\sin(2x^2+2)dx[/tex]
Se face schimbarea de variabilă
[tex]2x^2+2=t\Rightarrow 4xdx=dt[/tex]
[tex]I(t)=\displaystyle\int\sin tdt=-\cos t+\mathcal{C}[/tex]
[tex]I(x)=-\cos(2x^2+2)+\mathcal{C}[/tex]
g)
[tex]\displaystyle\int\tan x(\tan^2x+1)dx=\int\tan x\cdot\dfrac{1}{\cos^2x}}dx=\int\tan x(\tan x)'dx=\\=\dfrac{\tan^2x}{2}+\mathcal{C}[/tex]
Explicație pas cu pas: