Question

How do I calculate the integral?

Answer 1

http://www.integral-calculator.com/#

Maybe this website will help?

Answer 2

Thanks for the help! But I actually want to know the process of solving the integral.

Answer 3

Well post your question :)

Answer 4

There are many methods that can be employed ... which makes your question rather vague

Answer 5

\[Let I=\int\limits \sin \left( 4x \right)e ^{-x}dx\]
\[=\sin \left( 4x \right)\left( \frac{ e ^{-x} }{-1 } \right)-\int\limits 4\cos \left( 4x \right)\frac{ e ^{-x} }{-1 }dx\]
\[=-\sin \left( 4x \right)e ^{-x}+4\left[ \cos \left( 4x \right)\frac{ e ^{-x} }{-1 }-\int\limits \left( -4\sin \left( 4x \right) \right)\frac{ e ^{-x} }{-1 } \right]dx\]
\[or I=\left( -\sin \left( 4x \right)-4\cos \left( 4x \right)e ^{-x}-16 I \right)\]
\[17 I=-\left( \sin \left( 4x \right) +4 \cos \left( 4x \right)\right)e ^{-x}\]
calculate I

Answer 6

integrate twice by parts