What is the integral of 5x^3+e^x-cos(x) ?

The integral of 5x^3+e^x-cos(x) is (5x^4)/4+e^x-sin(x)+C

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integral of 5x^3+e^x-cos(x)

\int 5 x^{3} + e^{x} - cos (x) d x

\frac{5 x ^{4}}{4} + e^{x} - sin (x) + C

Solution steps

\int 5 x^{3} + e^{x} - cos (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 5 x^{3} d x + \int e^{x} d x - \int cos (x) d x

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

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

\int cos (x) d x = sin (x)

= \frac{5 x ^{4}}{4} + e^{x} - sin (x)

Add a constant to the solution

= \frac{5 x ^{4}}{4} + e^{x} - sin (x) + C

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What is the integral of 5x^3+e^x-cos(x) ?
The integral of 5x^3+e^x-cos(x) is (5x^4)/4+e^x-sin(x)+C