$\int\frac{e^x(1+x)}{\cos^2(xe^x)}dx=$
Answer & explanation
Correct answer: option 4
Put $xe^x=t,(e^x+xe^x)dx=dt$ to get: $\int\frac{e^x(1+x)}{\cos^2(xe^x)}dx=\int\frac{dt}{\cos^2(t)}=\int\sec^2(t)=\tan(t)=\tan(xe^x)+C$
$\int\frac{e^x(1+x)}{\cos^2(xe^x)}dx=$
Correct answer: option 4
Put $xe^x=t,(e^x+xe^x)dx=dt$ to get: $\int\frac{e^x(1+x)}{\cos^2(xe^x)}dx=\int\frac{dt}{\cos^2(t)}=\int\sec^2(t)=\tan(t)=\tan(xe^x)+C$