What is the integral of [(100)/(25+(5y)^2)+e^4] ?

The integral of [(100)/(25+(5y)^2)+e^4] is 4arctan(y)+e^4y+C

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integral of [(100)/(25+(5y)^2)+e^4]

\int [\frac{100}{25 + ( 5 y ) ^{2}} + e^{4}] d y

4 arctan (y) + e^{4} y + C

Solution steps

\int \frac{100}{25 + ( 5 y ) ^{2}} + e^{4} d y

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{100}{25 + ( 5 y ) ^{2}} d y + \int e^{4} d y

\int \frac{100}{25 + ( 5 y ) ^{2}} d y = 4 arctan (y)

\int e^{4} d y = e^{4} y

= 4 arctan (y) + e^{4} y

Add a constant to the solution

= 4 arctan (y) + e^{4} y + C

y^{^{'}} = e^{2 x} + 3 y

\int \frac{1}{x ^{2} + a ^{2}} d x

f (x) = 5 x - x^{2}, at x = 1

y^{^{'}} = 2 (1 + x) (1 + y^{2}), y (0) = 0

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

What is the integral of [(100)/(25+(5y)^2)+e^4] ?
The integral of [(100)/(25+(5y)^2)+e^4] is 4arctan(y)+e^4y+C