What is the integral of (sin(x)-\sqrt[4]{x}-e^x+18) ?

The integral of (sin(x)-\sqrt[4]{x}-e^x+18) is -cos(x)-4/5 x^{5/4}-e^x+18x+C

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integral of (sin(x)-\sqrt[4]{x}-e^x+18)

\int (sin (x) - 4 x - e^{x} + 18) d x

- cos (x) - \frac{4}{5} x^{\frac{5}{4}} - e^{x} + 18 x + C

Solution steps

\int sin (x) - 4 x - e^{x} + 18 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 sin (x) d x - \int 4 x d x - \int e^{x} d x + \int 18 d x

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

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

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

\int 18 d x = 18 x

= - cos (x) - \frac{4}{5} x^{\frac{5}{4}} - e^{x} + 18 x

Add a constant to the solution

= - cos (x) - \frac{4}{5} x^{\frac{5}{4}} - e^{x} + 18 x + C

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What is the integral of (sin(x)-\sqrt[4]{x}-e^x+18) ?
The integral of (sin(x)-\sqrt[4]{x}-e^x+18) is -cos(x)-4/5 x^{5/4}-e^x+18x+C