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Popular >

integral of x^2+kx+1

Solution

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

Solution

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

Solution steps

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

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

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

\int 1 d x = x

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

Add a constant to the solution

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

Popular Examples

tangent of 12(x-1/x)^4,\at x=2 tangent of

12 (x - \frac{1}{x})^{4}, at x = 2

derivative of 5+4x-x^3

\frac{d}{d x} (5 + 4 x - x^{3})

area x^2-1,-1,6 area

x^{2} - 1, - 1, 6

derivative of y=(5x^4-3x^3)(3x^2-7x^3)derivative of

y = (5 x^{4} - 3 x^{3}) (3 x^{2} - 7 x^{3})

integral of (3z^2)/y

\int \frac{3 z ^{2}}{y} d y

Frequently Asked Questions (FAQ)

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