Question:
Integrate the function: \(e^x(sinx+cosx)\)
Integrate the function: \(e^x(sinx+cosx)\)
Updated On: Oct 4, 2023
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Solution and Explanation
The correct answer is: \(∴I=e^x sinx+C\)
Let \(I=∫e^x(sinx+cosx)dx\)
Let \(ƒ(x)=sinx\)
\(⧠ƒ'(x)=cosx\)
\(⧠I=∫e^x[{ƒ(x)+ƒ'(x)}]dx\)
It is known that,\(∫e^x[{ƒ(x)+ƒ'(x)}]dx=e^x ƒ(x)+C\)
\(∴I=e^x sinx+C\)
Let \(I=∫e^x(sinx+cosx)dx\)
Let \(ƒ(x)=sinx\)
\(⧠ƒ'(x)=cosx\)
\(⧠I=∫e^x[{ƒ(x)+ƒ'(x)}]dx\)
It is known that,\(∫e^x[{ƒ(x)+ƒ'(x)}]dx=e^x ƒ(x)+C\)
\(∴I=e^x sinx+C\)
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For examples,
