What is the integral of (y^2cos(x)+cos(y)) ?

The integral of (y^2cos(x)+cos(y)) is cos(y)x+y^2sin(x)+C

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integral of (y^2cos(x)+cos(y))

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

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

Solution steps

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

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

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

= cos (y) x + y^{2} sin (x)

Add a constant to the solution

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

e^{\frac{1}{x}}

\int \frac{( 3 x ^{4} + 2 x ^{2} )}{( x ^{2} + 1 )} d x

\int \frac{x ^{2} + 6 x + 4}{x ^{3} + 9 x ^{2} + 12 x + 9} d x

\int 3 x^{3} - 2 \cdot (6 x^{2}) d x

\int 2 x^{\frac{4}{5}} d x

What is the integral of (y^2cos(x)+cos(y)) ?
The integral of (y^2cos(x)+cos(y)) is cos(y)x+y^2sin(x)+C