What is the integral of 3e^x-5sin(x) ?

The integral of 3e^x-5sin(x) is 3e^x+5cos(x)+C

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integral of 3e^x-5sin(x)

\int 3 e^{x} - 5 sin (x) d x

3 e^{x} + 5 cos (x) + C

Solution steps

\int 3 e^{x} - 5 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 3 e^{x} d x - \int 5 sin (x) d x

\int 3 e^{x} d x = 3 e^{x}

\int 5 sin (x) d x = - 5 cos (x)

= 3 e^{x} - (- 5 cos (x))

Simplify

= 3 e^{x} + 5 cos (x)

Add a constant to the solution

= 3 e^{x} + 5 cos (x) + C

\int - 4 x^{2} ln (4 x) d x

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\int \frac{y ^{2}}{( y ^{2} - 1 ) ^{\frac{3}{2}}} d y

\int \frac{3 x ^{2} + 2}{x} d x

\int (t e^{t} + t) d t

What is the integral of 3e^x-5sin(x) ?
The integral of 3e^x-5sin(x) is 3e^x+5cos(x)+C