What is the integral of y^2e^ycos(x) ?

The integral of y^2e^ycos(x) is y^2e^ysin(x)+C

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integral of y^2e^ycos(x)

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= y^{2} e^{y} \cdot \int cos (x) d x

Use the common integral:

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

= y^{2} e^{y} sin (x)

Add a constant to the solution

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

\int \frac{x ^{3}}{x ^{8} + 9} d x

\int x^{2} 2 x^{3} + 4 d x

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

\int tan (v) d v

\int 8 x^{3} y d x

What is the integral of y^2e^ycos(x) ?
The integral of y^2e^ycos(x) is y^2e^ysin(x)+C