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Popular Calculus >

integral of e^{3x}-y

Solution

\int e^{3 x} - y d x

Solution

- y x + \frac{1}{3} e^{3 x} + C

Solution steps

\int e^{3 x} - 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 y d x + \int e^{3 x} d x

\int y d x = y x

\int e^{3 x} d x = \frac{1}{3} e^{3 x}

= - y x + \frac{1}{3} e^{3 x}

Add a constant to the solution

= - y x + \frac{1}{3} e^{3 x} + C

Graph

Popular Examples

integral of e^{ax}cos(nx)

\int e^{a x} cos (n x) d x

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

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

integral of cos((npix)/pi)

\int cos (\frac{nπ x}{π}) d x

integral of (3x)/(x-1)

\int \frac{3 x}{x - 1} d x

integral of 4cos(1/4 pix)

\int 4 cos (\frac{1}{4} π x) d x

Frequently Asked Questions (FAQ)

What is the integral of e^{3x}-y ?
The integral of e^{3x}-y is -yx+1/3 e^{3x}+C