What is the integral of (4x^3+x^2+5) ?

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

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integral of (4x^3+x^2+5)

\int (4 x^{3} + x^{2} + 5) d x

x^{4} + \frac{x ^{3}}{3} + 5 x + C

Solution steps

\int 4 x^{3} + x^{2} + 5 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 4 x^{3} d x + \int x^{2} d x + \int 5 d x

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

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

\int 5 d x = 5 x

= x^{4} + \frac{x ^{3}}{3} + 5 x

Add a constant to the solution

= x^{4} + \frac{x ^{3}}{3} + 5 x + C

\frac{\partial}{\partial y} (a x^{2} + b y^{2})

\int x (1 + x)^{\frac{2}{3}} d x

y = cos (x), x = \frac{π}{2}, x = 2 π, y = 0

n = 0 \sum \infty \frac{2}{3} (\frac{1}{3})^{n}

\int \frac{7 - x}{x ^{2} - 4 x + 4} d x

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