What is the integral of x^4+10x^2+25 ?

The integral of x^4+10x^2+25 is (x^5)/5+(10x^3)/3+25x+C

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integral of x^4+10x^2+25

\int x^{4} + 10 x^{2} + 25 d x

\frac{x ^{5}}{5} + \frac{10 x ^{3}}{3} + 25 x + C

Solution steps

\int x^{4} + 10 x^{2} + 25 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 10 x^{2} d x + \int 25 d x

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

\int 10 x^{2} d x = \frac{10 x ^{3}}{3}

\int 25 d x = 25 x

= \frac{x ^{5}}{5} + \frac{10 x ^{3}}{3} + 25 x

Add a constant to the solution

= \frac{x ^{5}}{5} + \frac{10 x ^{3}}{3} + 25 x + C

y^{^{'}} + \frac{1}{2} y = 17 sin (2 t)

y = 4^{9^{x^{2}}}

\int \frac{x ^{2} + 8 x - 1}{x ^{3} - x} d x

x \to - 1 lim (2 x^{2} - \frac{2}{x - 1})

\frac{\partial}{\partial x} (x^{9} y^{4} - x^{6} + y^{8})

What is the integral of x^4+10x^2+25 ?
The integral of x^4+10x^2+25 is (x^5)/5+(10x^3)/3+25x+C