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

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

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

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

\frac{5 x ^{4}}{4} + 3 sin (x) + C

Solution steps

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

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

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

= \frac{5 x ^{4}}{4} + 3 sin (x)

Add a constant to the solution

= \frac{5 x ^{4}}{4} + 3 sin (x) + C

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