What is the integral of (2e^{2x}+12x^3+4x) ?

The integral of (2e^{2x}+12x^3+4x) is e^{2x}+3x^4+2x^2+C

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integral of (2e^{2x}+12x^3+4x)

\int (2 e^{2 x} + 12 x^{3} + 4 x) d x

e^{2 x} + 3 x^{4} + 2 x^{2} + C

Solution steps

\int 2 e^{2 x} + 12 x^{3} + 4 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 e^{2 x} d x + \int 12 x^{3} d x + \int 4 x d x

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

\int 12 x^{3} d x = 3 x^{4}

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

= e^{2 x} + 3 x^{4} + 2 x^{2}

Add a constant to the solution

= e^{2 x} + 3 x^{4} + 2 x^{2} + C

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

\frac{\partial}{\partial t} (t + sin (t - 1))

\int 3 tan^{3} (2 x) sec^{5} (2 x) d x

x^{3} \cdot y^{^{'}} = x

[(z - 1)^{3} (z + 1)^{2}]

What is the integral of (2e^{2x}+12x^3+4x) ?
The integral of (2e^{2x}+12x^3+4x) is e^{2x}+3x^4+2x^2+C