What is the integral of 2x^4+e^{2x}+sin(3x) ?

The integral of 2x^4+e^{2x}+sin(3x) is (2x^5)/5+1/2 e^{2x}-1/3 cos(3x)+C

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integral of 2x^4+e^{2x}+sin(3x)

\int 2 x^{4} + e^{2 x} + sin (3 x) d x

\frac{2 x ^{5}}{5} + \frac{1}{2} e^{2 x} - \frac{1}{3} cos (3 x) + C

Solution steps

\int 2 x^{4} + e^{2 x} + sin (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 2 x^{4} d x + \int e^{2 x} d x + \int sin (3 x) d x

\int 2 x^{4} d x = \frac{2 x ^{5}}{5}

\int e^{2 x} d x = \frac{1}{2} e^{2 x}

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

= \frac{2 x ^{5}}{5} + \frac{1}{2} e^{2 x} - \frac{1}{3} cos (3 x)

Add a constant to the solution

= \frac{2 x ^{5}}{5} + \frac{1}{2} e^{2 x} - \frac{1}{3} cos (3 x) + C

f (x) = \frac{4}{1 + x ^{2}}

\int x^{2} \cdot e^{2 x} d x

y^{^{'}} = 1 + x - y - x y

x \to 2 lim (\frac{sin ( 2 x )}{x})

y = x (81.9)

What is the integral of 2x^4+e^{2x}+sin(3x) ?
The integral of 2x^4+e^{2x}+sin(3x) is (2x^5)/5+1/2 e^{2x}-1/3 cos(3x)+C