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

The integral of (sqrt(x^5))/(x^3)-e^x-cos(3) is 2sqrt(x)-e^x-cos(3)x+C

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integral of (sqrt(x^5))/(x^3)-e^x-cos(3)

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

2 x - e^{x} - cos (3) x + C

Solution steps

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

\int \frac{x ^{5}}{x ^{3}} d x = 2 x

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

\int cos (3) d x = cos (3) x

= 2 x - e^{x} - cos (3) x

Add a constant to the solution

= 2 x - e^{x} - cos (3) x + C

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\int 4 x + \frac{1}{5} + \frac{1}{x} d x

\int - x e^{- y} d y

What is the integral of (sqrt(x^5))/(x^3)-e^x-cos(3) ?
The integral of (sqrt(x^5))/(x^3)-e^x-cos(3) is 2sqrt(x)-e^x-cos(3)x+C