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Popular >

integral of x^2+3x+1

Solution

\int x^{2} + 3 x + 1 d x

Solution

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

Solution steps

\int x^{2} + 3 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 3 x d x + \int 1 d x

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

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

\int 1 d x = x

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

Add a constant to the solution

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

Popular Examples

integral of 2sqrt(y)

\int 2 y d y

integral of xsin^2(7x)

\int x sin^{2} (7 x) d x

tangent of f(x)= 2/x ,(3, 2/3)tangent of

f (x) = \frac{2}{x}, (3, \frac{2}{3})

derivative of f(x)=(x+6)/(x-4)derivative of

f (x) = \frac{x + 6}{x - 4}

taylor 1+x taylor

1 + x

Frequently Asked Questions (FAQ)

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