What is the integral of (136)/(1+0.25(x-4.5)^2)+28 ?

The integral of (136)/(1+0.25(x-4.5)^2)+28 is 272arctan(0.5(x-4.5))+28x+C

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integral of (136)/(1+0.25(x-4.5)^2)+28

\int \frac{136}{1 + 0.25 ( x - 4.5 ) ^{2}} + 28 d x

272 arctan (0.5 (x - 4.5)) + 28 x + C

Solution steps

\int \frac{136}{1 + 0.25 ( x - 4.5 ) ^{2}} + 28 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{136}{1 + 0.25 ( x - 4.5 ) ^{2}} d x + \int 28 d x

\int \frac{136}{1 + 0.25 ( x - 4.5 ) ^{2}} d x = 272 arctan (0.5 (x - 4.5))

\int 28 d x = 28 x

= 272 arctan (0.5 (x - 4.5)) + 28 x

Add a constant to the solution

= 272 arctan (0.5 (x - 4.5)) + 28 x + C

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What is the integral of (136)/(1+0.25(x-4.5)^2)+28 ?
The integral of (136)/(1+0.25(x-4.5)^2)+28 is 272arctan(0.5(x-4.5))+28x+C