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Popular >

integral of (x^3+1)

Solution

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

Solution

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

Solution steps

\int x^{3} + 1 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^{3} d x + \int 1 d x

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

\int 1 d x = x

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

Add a constant to the solution

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

Popular Examples

integral of (sqrt(25x^2-4))/x

\int \frac{25 x ^{2} - 4}{x} d x

derivative of arccos(6x^2)

\frac{d}{d x} (arccos (6 x^{2}))

(\partial)/(\partial x)(arccos(xy))

\frac{\partial}{\partial x} (arccos (x y))

(\partial)/(\partial x)(m/p+625 p/x)

\frac{\partial}{\partial x} (\frac{m}{p} + 625 \frac{p}{x})

derivative of e^{(3x^2/2})

\frac{d}{d x} (e^{\frac{3 x ^{2}}{2}})

Frequently Asked Questions (FAQ)

What is the integral of (x^3+1) ?
The integral of (x^3+1) is (x^4)/4+x+C