What is the integral of (3x^2tan(y)-(2y^3)/(x^3)) ?

The integral of (3x^2tan(y)-(2y^3)/(x^3)) is (y^3)/(x^2)+x^3tan(y)+C

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integral of (3x^2tan(y)-(2y^3)/(x^3))

\int (3 x^{2} tan (y) - \frac{2 y ^{3}}{x ^{3}}) d x

\frac{y ^{3}}{x ^{2}} + x^{3} tan (y) + C

Solution steps

\int 3 x^{2} tan (y) - \frac{2 y ^{3}}{x ^{3}} 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 \frac{2 y ^{3}}{x ^{3}} d x + \int 3 tan (y) x^{2} d x

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

\int 3 tan (y) x^{2} d x = x^{3} tan (y)

= - (- \frac{y ^{3}}{x ^{2}}) + x^{3} tan (y)

Simplify

= \frac{y ^{3}}{x ^{2}} + x^{3} tan (y)

Add a constant to the solution

= \frac{y ^{3}}{x ^{2}} + x^{3} tan (y) + C

f (x) = 3 csc (4 x)

(y^{4} - x^{2}) d y + x y d x = 0

x^{2} - 5 x

x y^{^{'}} + 4 y = 9 x^{5} + 2 x^{3}

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3 t}

What is the integral of (3x^2tan(y)-(2y^3)/(x^3)) ?
The integral of (3x^2tan(y)-(2y^3)/(x^3)) is (y^3)/(x^2)+x^3tan(y)+C