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Popular >

integral of x^2+6x+1

Solution

\int x^{2} + 6 x + 1 d x

Solution

\frac{x ^{3}}{3} + 3 x^{2} + x + C

Solution steps

\int x^{2} + 6 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 x^{2} d x + \int 6 x d x + \int 1 d x

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

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

\int 1 d x = x

= \frac{x ^{3}}{3} + 3 x^{2} + x

Add a constant to the solution

= \frac{x ^{3}}{3} + 3 x^{2} + x + C

Popular Examples

derivative of x/3 (2x+1^3)

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

integral of (3^x)/(3^x+2)

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

limit as x approaches 0 of 1/(e^{1/x)}

x \to 0 lim (\frac{1}{e ^{\frac{1}{x}}})

(\partial)/(\partial z)(x/z)

\frac{\partial}{\partial z} (\frac{x}{z})

derivative of g(x)=ln(xe^{-7x})derivative of

g (x) = ln (x e^{- 7 x})

Frequently Asked Questions (FAQ)

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