What is the integral of (8x^3-4csc^2(x)+e^x) ?

The integral of (8x^3-4csc^2(x)+e^x) is 2x^4+4cot(x)+e^x+C

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integral of (8x^3-4csc^2(x)+e^x)

\int (8 x^{3} - 4 csc^{2} (x) + e^{x}) d x

2 x^{4} + 4 cot (x) + e^{x} + C

Solution steps

\int 8 x^{3} - 4 csc^{2} (x) + e^{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 8 x^{3} d x - \int 4 csc^{2} (x) d x + \int e^{x} d x

\int 8 x^{3} d x = 2 x^{4}

\int 4 csc^{2} (x) d x = - 4 cot (x)

\int e^{x} d x = e^{x}

= 2 x^{4} - (- 4 cot (x)) + e^{x}

Simplify

= 2 x^{4} + 4 cot (x) + e^{x}

Add a constant to the solution

= 2 x^{4} + 4 cot (x) + e^{x} + C

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What is the integral of (8x^3-4csc^2(x)+e^x) ?
The integral of (8x^3-4csc^2(x)+e^x) is 2x^4+4cot(x)+e^x+C