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Popular >

integral of x^2-4x+7

Solution

\int x^{2} - 4 x + 7 d x

Solution

\frac{x ^{3}}{3} - 2 x^{2} + 7 x + C

Solution steps

\int x^{2} - 4 x + 7 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 4 x d x + \int 7 d x

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

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

\int 7 d x = 7 x

= \frac{x ^{3}}{3} - 2 x^{2} + 7 x

Add a constant to the solution

= \frac{x ^{3}}{3} - 2 x^{2} + 7 x + C

Popular Examples

limit as x approaches-1 of (x^2-3)/(1-x)

x \to - 1 lim (\frac{x ^{2} - 3}{1 - x})

(\partial)/(\partial x)(sin(x^2y-4xy^2))

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

integral of 7/((t^2+1)^{3/2)}

\int \frac{7}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

derivative of 4/(3x^2)derivative of

\frac{4}{3 x ^{2}}

tangent of f(x)=x^2-1/x ,(-1,0)tangent of

f (x) = x^{2} - \frac{1}{x}, (- 1, 0)

Frequently Asked Questions (FAQ)

What is the integral of x^2-4x+7 ?
The integral of x^2-4x+7 is (x^3)/3-2x^2+7x+C