What is the integral of-5sin(x)+\sqrt[4]{x}+5 ?

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

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integral of-5sin(x)+\sqrt[4]{x}+5

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

Solution steps

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 sin (x) d x = - 5 cos (x)

\int 5 d x = 5 x

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

Simplify

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

Add a constant to the solution

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

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