What is the integral of sec^2(pix)+e^{-3x} ?

The integral of sec^2(pix)+e^{-3x} is 1/pi tan(pix)-1/3 e^{-3x}+C

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integral of sec^2(pix)+e^{-3x}

\int sec^{2} (π x) + e^{- 3 x} d x

\frac{1}{π} tan (π x) - \frac{1}{3} e^{- 3 x} + C

Solution steps

\int sec^{2} (π x) + e^{- 3 x} 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 sec^{2} (π x) d x + \int e^{- 3 x} d x

\int sec^{2} (π x) d x = \frac{1}{π} tan (π x)

\int e^{- 3 x} d x = - \frac{1}{3} e^{- 3 x}

= \frac{1}{π} tan (π x) - \frac{1}{3} e^{- 3 x}

Add a constant to the solution

= \frac{1}{π} tan (π x) - \frac{1}{3} e^{- 3 x} + C

\int sec^{2} (2 a) x d x

\frac{1}{u}

\frac{1}{t}

\int \frac{1}{- x ^{2} - 8 x} d x

\int \frac{d}{1} (x sin (x)) d x

What is the integral of sec^2(pix)+e^{-3x} ?
The integral of sec^2(pix)+e^{-3x} is 1/pi tan(pix)-1/3 e^{-3x}+C