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

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

x \to 5 lim (5)

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

\int 3 x 2 x + 3 d x

\int cos^{3} (\frac{x}{8}) d x

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