What is the integral of ycos(xy)-3y^2+e^x ?

The integral of ycos(xy)-3y^2+e^x is e^x-3y^2x+sin(yx)+C

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integral of ycos(xy)-3y^2+e^x

\int y cos (x y) - 3 y^{2} + e^{x} d x

e^{x} - 3 y^{2} x + sin (y x) + C

Solution steps

\int y cos (x y) - 3 y^{2} + e^{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 e^{x} d x - \int 3 y^{2} d x + \int cos (y x) y d x

\int e^{x} d x = e^{x}

\int 3 y^{2} d x = 3 y^{2} x

\int cos (y x) y d x = sin (y x)

= e^{x} - 3 y^{2} x + sin (y x)

Add a constant to the solution

= e^{x} - 3 y^{2} x + sin (y x) + C

x = - 2, x = 3, y = x^{2} - 3, y = 2 x

e^{5 x + 5}, 0

\frac{d y}{d x} = (1 - 2 x) y^{2}

\int_{0}^{2} 2 π x (3 + \frac{x ^{2}}{3}) d x

f (x) = \frac{sin ( x ) + cos ( x )}{sin ( x ) - cos ( x )}

What is the integral of ycos(xy)-3y^2+e^x ?
The integral of ycos(xy)-3y^2+e^x is e^x-3y^2x+sin(yx)+C