What is the integral of 1/(e^3)x+sin(x) ?

The integral of 1/(e^3)x+sin(x) is (x^2)/(2e^3)-cos(x)+C

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integral of 1/(e^3)x+sin(x)

integral

\frac{1}{e ^{3}} x + sin (x)

\frac{x ^{2}}{2 e ^{3}} - cos (x) + C

Solution steps

\int \frac{1}{e ^{3}} x + sin (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 \frac{1}{e ^{3}} x d x + \int sin (x) d x

\int \frac{1}{e ^{3}} x d x = \frac{x ^{2}}{2 e ^{3}}

\int sin (x) d x = - cos (x)

= \frac{x ^{2}}{2 e ^{3}} - cos (x)

Add a constant to the solution

= \frac{x ^{2}}{2 e ^{3}} - cos (x) + C

(2 - 3 x^{2})^{3}

\frac{1}{( x + 2 )}

cos^{- 2} (x)

1 - cos (6 x)

(5 x - 4)^{- 3}

What is the integral of 1/(e^3)x+sin(x) ?
The integral of 1/(e^3)x+sin(x) is (x^2)/(2e^3)-cos(x)+C