What is the integral of (2x^4+30e^{5x}+sqrt(x)+8) ?

The integral of (2x^4+30e^{5x}+sqrt(x)+8) is (2x^5)/5+6e^{5x}+2/3 x^{3/2}+8x+C

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integral of (2x^4+30e^{5x}+sqrt(x)+8)

\int (2 x^{4} + 30 e^{5 x} + x + 8) d x

\frac{2 x ^{5}}{5} + 6 e^{5 x} + \frac{2}{3} x^{\frac{3}{2}} + 8 x + C

Solution steps

\int 2 x^{4} + 30 e^{5 x} + x + 8 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 30 e^{5 x} d x + \int x d x + \int 8 d x

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

\int 30 e^{5 x} d x = 6 e^{5 x}

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

\int 8 d x = 8 x

= \frac{2 x ^{5}}{5} + 6 e^{5 x} + \frac{2}{3} x^{\frac{3}{2}} + 8 x

Add a constant to the solution

= \frac{2 x ^{5}}{5} + 6 e^{5 x} + \frac{2}{3} x^{\frac{3}{2}} + 8 x + C

What is the integral of (2x^4+30e^{5x}+sqrt(x)+8) ?
The integral of (2x^4+30e^{5x}+sqrt(x)+8) is (2x^5)/5+6e^{5x}+2/3 x^{3/2}+8x+C