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Popular Calculus >

integral of a+bx^2

Solution

\int a + b x^{2} d x

Solution

a x + \frac{b x ^{3}}{3} + C

Solution steps

\int a + b 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 a d x + \int b x^{2} d x

\int a d x = a x

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

= a x + \frac{b x ^{3}}{3}

Add a constant to the solution

= a x + \frac{b x ^{3}}{3} + C

Graph

Popular Examples

integral of 2/(sqrt(x^2-1))

\int \frac{2}{x ^{2} - 1} d x

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\int \frac{e ^{2 x}}{e ^{2 x} - 8} d x

integral of (2x^2-4x-3)/(x^2)

\int \frac{2 x ^{2} - 4 x - 3}{x ^{2}} d x

integral of tan^2(x)sec^2(x)

in t e g r a l tan^{2} (x) sec^{2} (x)

integral of 95-(3x^2+2x+10)

\int 95 - (3 x^{2} + 2 x + 10) d x

Frequently Asked Questions (FAQ)

What is the integral of a+bx^2 ?
The integral of a+bx^2 is ax+(bx^3)/3+C