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Popular >

integral from 0 to x of 2x+1

Solution

\int_{0}^{x} 2 x + 1 d x

Solution

x^{2} + x

Solution steps

\int_{0}^{x} 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_{0}^{x} 2 x d x + \int_{0}^{x} 1 d x

\int_{0}^{x} 2 x d x = x^{2}

\int_{0}^{x} 1 d x = x

= x^{2} + x

Popular Examples

integral from pi/6 to pi/4 of ln(sin(x))

\int_{\frac{π}{6}}^{\frac{π}{4}} ln (sin (x)) d x

integral from-1 to 1 of x|2x-1|

\int_{- 1}^{1} x ∣ 2 x - 1 ∣ d x

integral from 0 to 1 of (x+1)e^{2x}

\int_{0}^{1} (x + 1) e^{2 x} d x

integral from 2 to 4 of x^3+4x^2

\int_{2}^{4} x^{3} + 4 x^{2} d x

integral from 0 to 1 of (x^4y+y^2)

\int_{0}^{1} (x^{4} y + y^{2}) d y

Frequently Asked Questions (FAQ)

What is the integral from 0 to x of 2x+1 ?
The integral from 0 to x of 2x+1 is x^2+x