Integral of 2x^(-3)+3sin(x) dx
The solution
Detail solution
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Integrate term-by-term:
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The integral of a constant times a function is the constant times the integral of the function:
∫3sin(x)dx=3∫sin(x)dx
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The integral of sine is negative cosine:
∫sin(x)dx=−cos(x)
So, the result is: −3cos(x)
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The integral of a constant times a function is the constant times the integral of the function:
∫x32dx=2∫x31dx
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The integral of xn is n+1xn+1 when n=−1:
∫x31dx=−2x21
So, the result is: −x21
The result is: −3cos(x)−x21
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Add the constant of integration:
−3cos(x)−x21+constant
The answer is:
−3cos(x)−x21+constant
The answer (Indefinite)
[src]
/
|
| /2 \ 1
| |-- + 3*sin(x)| dx = C - -- - 3*cos(x)
| | 3 | 2
| \x / x
|
/
−3cosx−x21
The graph
Use the examples entering the upper and lower limits of integration.