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

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

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

4 x - 16

y^{^{''}} + 10 y^{^{'}} + 20 y = 0

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