What is the integral of x^4+cos(3x) ?

The integral of x^4+cos(3x) is (x^5)/5+1/3 sin(3x)+C

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integral of x^4+cos(3x)

\int x^{4} + cos (3 x) d x

\frac{x ^{5}}{5} + \frac{1}{3} sin (3 x) + C

Solution steps

\int x^{4} + cos (3 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 x^{4} d x + \int cos (3 x) d x

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

\int cos (3 x) d x = \frac{1}{3} sin (3 x)

= \frac{x ^{5}}{5} + \frac{1}{3} sin (3 x)

Add a constant to the solution

= \frac{x ^{5}}{5} + \frac{1}{3} sin (3 x) + C

\frac{\partial}{\partial x} (ln (5 x^{2} y^{2}))

\frac{d}{d x} (\frac{e ^{x^{3}}}{sin ( 2 x )})

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 e^{2 x}

y = x, y = 3 x, x + y = 4

n = 1 \sum \infty 0.9 9^{n}

What is the integral of x^4+cos(3x) ?
The integral of x^4+cos(3x) is (x^5)/5+1/3 sin(3x)+C