What is the integral of e^{3x}-sin(x)+7/(1+x^2) ?

The integral of e^{3x}-sin(x)+7/(1+x^2) is 1/3 e^{3x}+cos(x)+7arctan(x)+C

Popular >

integral of e^{3x}-sin(x)+7/(1+x^2)

\int e^{3 x} - sin (x) + \frac{7}{1 + x ^{2}} d x

\frac{1}{3} e^{3 x} + cos (x) + 7 arctan (x) + C

Solution steps

\int e^{3 x} - sin (x) + \frac{7}{1 + x ^{2}} 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 e^{3 x} d x - \int sin (x) d x + \int \frac{7}{1 + x ^{2}} d x

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

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

\int \frac{7}{1 + x ^{2}} d x = 7 arctan (x)

= \frac{1}{3} e^{3 x} - (- cos (x)) + 7 arctan (x)

Simplify

= \frac{1}{3} e^{3 x} + cos (x) + 7 arctan (x)

Add a constant to the solution

= \frac{1}{3} e^{3 x} + cos (x) + 7 arctan (x) + C

\frac{\partial}{\partial x} (ln (x^{2} + 2 y^{2} + 2))

y^{^{'}} t^{4} = 0

\int_{0}^{π} x^{2} sin (x) d x

e^{- 4 t} \cdot cos (t)

\int (- \frac{2}{x ^{2}} + 3 x) d x

What is the integral of e^{3x}-sin(x)+7/(1+x^2) ?
The integral of e^{3x}-sin(x)+7/(1+x^2) is 1/3 e^{3x}+cos(x)+7arctan(x)+C