What is the integral of y=(e^(13x)+sin x)/10
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If you mean that you required the integral of y = (e^(13x)+sin x)/10, the result is.
y = (e^(13x)+sin x)/10
Int [ y dx] = Int [ (e^(13x)+sin x)/10 dx]
=> (1/10)* Int [ (e^(13x)+sin x) dx]
=> (1/10)*[ Int [ e^(13x) dx] +Int [sin x dx] ]
=> (1/10)*[ e^(13x)/13 - cos x ] + C
The integral of (e^(13x)+sin x)/10 is (1/10)*[ e^(13x)/13 - cos x ] + C
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In other words, we'll have to calculate the indefinite integral of y.
Int [e^(13x)+sin x]dx/10 = (1/10)*[Inte^(13x)dx + Int sin x dx ]
We'll calculate each term of the sum:
Inte^(13x)dx = e^(13x)/13 + c
Int sin x dx = -cos x + c
We'll substitute the integrals by their results and we'll get:
Int [e^(13x)+sin x]dx/10 = [e^(13x)]/130 - (cos x)/10 + c
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