What is the integral of ((3x^4)/pi+10cos(x)+1/(e^x)) ?

The integral of ((3x^4)/pi+10cos(x)+1/(e^x)) is 3/pi*(x^5)/5+10sin(x)-1/(e^x)+C

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integral of ((3x^4)/pi+10cos(x)+1/(e^x))

\int (\frac{3 x ^{4}}{π} + 10 cos (x) + \frac{1}{e ^{x}}) d x

\frac{3}{π} \cdot \frac{x ^{5}}{5} + 10 sin (x) - \frac{1}{e ^{x}} + C

Solution steps

\int \frac{3 x ^{4}}{π} + 10 cos (x) + \frac{1}{e ^{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{3 x ^{4}}{π} d x + \int 10 cos (x) d x + \int \frac{1}{e ^{x}} d x

\int \frac{3 x ^{4}}{π} d x = \frac{3}{π} \cdot \frac{x ^{5}}{5}

\int 10 cos (x) d x = 10 sin (x)

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

= \frac{3}{π} \cdot \frac{x ^{5}}{5} + 10 sin (x) - \frac{1}{e ^{x}}

Add a constant to the solution

= \frac{3}{π} \cdot \frac{x ^{5}}{5} + 10 sin (x) - \frac{1}{e ^{x}} + C

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What is the integral of ((3x^4)/pi+10cos(x)+1/(e^x)) ?
The integral of ((3x^4)/pi+10cos(x)+1/(e^x)) is 3/pi*(x^5)/5+10sin(x)-1/(e^x)+C