Question

Write a value of

\[\int e^x \left( \sin x + \cos x \right) \text{ dx}\]

 

Answer 1

Let I=\[\int\] e^x (sin x + cos x) dx

Let e^x sin x = t
⇒ (e^x . sin x + e^x cos x) dx = dt

\[\therefore I = \int dt\]
\[ = t + C\]
\[ = e^x \sin x + C \left( \because t = e^x \sin x \right)\]