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Popular >

integral of (x^2)/2+1

Solution

\int \frac{x ^{2}}{2} + 1 d x

Solution

\frac{x ^{3}}{6} + x + C

Solution steps

\int \frac{x ^{2}}{2} + 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 \frac{x ^{2}}{2} d x + \int 1 d x

\int \frac{x ^{2}}{2} d x = \frac{x ^{3}}{6}

\int 1 d x = x

= \frac{x ^{3}}{6} + x

Add a constant to the solution

= \frac{x ^{3}}{6} + x + C

Popular Examples

(\partial)/(\partial x)(xy+81)

\frac{\partial}{\partial x} (x y + 81)

sum from n=1 to infinity of 5/(n(n+3))

n = 1 \sum \infty \frac{5}{n ( n + 3 )}

laplacetransform {1}laplace transform

{1}

integral of ((x^2-x+5)/x)

\int (\frac{x ^{2} - x + 5}{x}) d x

\frac{d y}{d x} = - y + 5

Frequently Asked Questions (FAQ)

What is the integral of (x^2)/2+1 ?
The integral of (x^2)/2+1 is (x^3)/6+x+C