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Popular >

integral of 1/2 x+1

Solution

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

Solution

\frac{x ^{2}}{4} + x + C

Solution steps

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

\int \frac{1}{2} x d x = \frac{x ^{2}}{4}

\int 1 d x = x

= \frac{x ^{2}}{4} + x

Add a constant to the solution

= \frac{x ^{2}}{4} + x + C

Graph

Popular Examples

integral of (1-t^2)/(1+t^2)

\int \frac{1 - t ^{2}}{1 + t ^{2}} d t

integral of 1/((y^2-y))

\int \frac{1}{( y ^{2} - y )} d y

x^2y^{''}=(y^')^2

x^{2} y^{^{''}} = (y^{^{'}})^{2}

(\partial)/(\partial x)(3y^3-4yx^2)

\frac{\partial}{\partial x} (3 y^{3} - 4 y x^{2})

integral from 0 to 7 of f(x)

\int_{0}^{7} f (x) d x

Frequently Asked Questions (FAQ)

What is the integral of 1/2 x+1 ?
The integral of 1/2 x+1 is (x^2)/4+x+C