CUET Preparation Today
$\int\frac{e^x(1+x)}{\cos^2(xe^x)}dx=$ |
$\tan(e^x)+x+C$ $\cos(xe^x)$ $\sec(e^xx)+C$ $\tan(e^xx)+C$ |
$\tan(e^xx)+C$ |
Put $xe^x=t,(e^x+xe^x)dx=dt$ to get: $\int\frac{e^x(1+x)}{\cos^2(xe^x)}dx=\int\frac{dt}{\cos^2(t)}=\int\sec^2(t)=\tan(t)=\tan(xe^x)+C$ |
