What is the integral of (e^x+cos(x)+t+1/t) ?

The integral of (e^x+cos(x)+t+1/t) is sin(x)+x/t+tx+e^x+C

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integral of (e^x+cos(x)+t+1/t)

\int (e^{x} + cos (x) + t + \frac{1}{t}) d x

sin (x) + \frac{x}{t} + t x + e^{x} + C

Solution steps

\int e^{x} + cos (x) + t + \frac{1}{t} 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 cos (x) d x + \int \frac{1}{t} d x + \int t d x + \int e^{x} d x

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

\int \frac{1}{t} d x = \frac{x}{t}

\int t d x = t x

\int e^{x} d x = e^{x}

= sin (x) + \frac{x}{t} + t x + e^{x}

Add a constant to the solution

= sin (x) + \frac{x}{t} + t x + e^{x} + C

\frac{\partial}{\partial x} (\frac{3 x}{2 + y})

\frac{d}{d x} (\frac{x cos ( x ) - sin ( x )}{6 x ^{2}})

x^{2} ln (9 x)

\frac{d}{d x} (9 x^{2} + 5)

\int_{0}^{0.5} 8 x - \frac{1}{8} x d x

What is the integral of (e^x+cos(x)+t+1/t) ?
The integral of (e^x+cos(x)+t+1/t) is sin(x)+x/t+tx+e^x+C