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Popular >

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

Popular Examples

integral of (y^2)/((y+1))

\int \frac{y ^{2}}{( y + 1 )} d y

integral of (sin(ax))/a

\int \frac{sin ( a x )}{a} d x

\int n d n

integral of sin(x)sqrt((1+cos(x))^3)

\int sin (x) (1 + cos (x))^{3} d x

integral of (2x^5-7x^3+4)

\int (2 x^{5} - 7 x^{3} + 4) d x

Frequently Asked Questions (FAQ)

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