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Popular >

integral of 1+x+5x^2

Solution

\int 1 + x + 5 x^{2} d x

Solution

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

Solution steps

\int 1 + x + 5 x^{2} 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 1 d x + \int x d x + \int 5 x^{2} d x

\int 1 d x = x

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

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

Add a constant to the solution

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

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integral of x^2-9x+2

\int x^{2} - 9 x + 2 d x

Frequently Asked Questions (FAQ)

What is the integral of 1+x+5x^2 ?
The integral of 1+x+5x^2 is x+(x^2)/2+(5x^3)/3+C