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Popular >

integral of a+bx

Solution

\int a + b x d x

Solution

a x + \frac{b x ^{2}}{2} + C

Solution steps

\int a + b x 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 d x

\int a d x = a x

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

= a x + \frac{b x ^{2}}{2}

Add a constant to the solution

= a x + \frac{b x ^{2}}{2} + C

Popular Examples

limit as x approaches 0 of (3|x|)/(x^2)

x \to 0 lim (\frac{3 ∣ x ∣}{x ^{2}})

integral of ((65x+7))/((8x+1)(x-1))

\int \frac{( 65 x + 7 )}{( 8 x + 1 ) ( x - 1 )} d x

integral of (10)/(e^{x/2)}

\int \frac{10}{e ^{\frac{x}{2}}} d x

integral of (tan^3(x))/(sec(x))

\int \frac{tan ^{3} ( x )}{sec ( x )} d x

(\partial)/(\partial y)(x^4y-x^2y^3)

\frac{\partial}{\partial y} (x^{4} y - x^{2} y^{3})

Frequently Asked Questions (FAQ)

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