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Integral of e^x cos(x)
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Tabular Integration of ∫e^x cos(x) dx:
Differentiate (D) e^x and Integrate (I) cos(x) repeatedly:
D: e^x, e^x, e^x, e^x
I: cos(x), -sin(x), -cos(x), sin(x)
Multiply diagonally and alternate signs:
(+) e^x * cos(x), (-) e^x * (-sin(x)), (+) e^x * (-cos(x)), (-) e^x * sin(x)
Add the products and their signs:
∫e^x cos(x) dx = e^x cos(x) + e^x sin(x) - e^x cos(x) - e^x sin(x) + C
Simplify the expression:
∫e^x cos(x) dx = (e^x)(cos(x) + sin(x)) + C
Remember to include a constant of integration (C) at the end.
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Differentiate (D) e^x and Integrate (I) cos(x) repeatedly:
D: e^x, e^x, e^x, e^x
I: cos(x), -sin(x), -cos(x), sin(x)
Multiply diagonally and alternate signs:
(+) e^x * cos(x), (-) e^x * (-sin(x)), (+) e^x * (-cos(x)), (-) e^x * sin(x)
Add the products and their signs:
∫e^x cos(x) dx = e^x cos(x) + e^x sin(x) - e^x cos(x) - e^x sin(x) + C
Simplify the expression:
∫e^x cos(x) dx = (e^x)(cos(x) + sin(x)) + C
Remember to include a constant of integration (C) at the end.
Please visit our Merch Stores and help support the spreading of knowledge:)
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