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Popular >

integral of x^2+3x+5

Solution

\int x^{2} + 3 x + 5 d x

Solution

\frac{x ^{3}}{3} + \frac{3 x ^{2}}{2} + 5 x + C

Solution steps

\int x^{2} + 3 x + 5 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 5 d x

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

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

\int 5 d x = 5 x

= \frac{x ^{3}}{3} + \frac{3 x ^{2}}{2} + 5 x

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{3 x ^{2}}{2} + 5 x + C

Graph

Popular Examples

integral of (21x^2)/(4(x^3+5)^{5/4)}

\int \frac{21 x ^{2}}{4 ( x ^{3} + 5 ) ^{\frac{5}{4}}} d x

integral of (6x-2)

\int (6 x - 2) d x

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\int (sin (x))^{4} (cos (x))^{3} d x

integral of 2(ln(x))

\int 2 (ln (x)) d x

integral of x+e^{-2x}

\int x + e^{- 2 x} d x

Frequently Asked Questions (FAQ)

What is the integral of x^2+3x+5 ?
The integral of x^2+3x+5 is (x^3)/3+(3x^2)/2+5x+C