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Popular Calculus >

integral of ax+by

Solution

\int a x + b y d x

Solution

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

Solution steps

\int a x + b y 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 x d x + \int b y d x

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

\int b y d x = b y x

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

Add a constant to the solution

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

Graph

Popular Examples

integral of (2)5^{x^2+7}

\int (2) 5^{x^{2} + 7} d x

integral of (x^3)/(3x^2+3)

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

integral of (2x+1)*(x^2+x+1)

\int (2 x + 1) \cdot (x^{2} + x + 1) d x

integral of e^{-2ix}

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

integral of 1/(2e^x+3)

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

Frequently Asked Questions (FAQ)

What is the integral of ax+by ?
The integral of ax+by is (ax^2)/2+byx+C