What is the integral of 2sqrt(x)-5^x+3/x ?

The integral of 2sqrt(x)-5^x+3/x is 4/3 x^{3/2}-(5^x)/(ln(5))+3ln|x|+C

Popular >

integral of 2sqrt(x)-5^x+3/x

\int 2 x - 5^{x} + \frac{3}{x} d x

\frac{4}{3} x^{\frac{3}{2}} - \frac{5 ^{x}}{ln ( 5 )} + 3 ln ∣ x ∣ + C

Solution steps

\int 2 x - 5^{x} + \frac{3}{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 2 x d x - \int 5^{x} d x + \int \frac{3}{x} d x

\int 2 x d x = \frac{4}{3} x^{\frac{3}{2}}

\int 5^{x} d x = \frac{5 ^{x}}{ln ( 5 )}

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= \frac{4}{3} x^{\frac{3}{2}} - \frac{5 ^{x}}{ln ( 5 )} + 3 ln ∣ x ∣

Add a constant to the solution

= \frac{4}{3} x^{\frac{3}{2}} - \frac{5 ^{x}}{ln ( 5 )} + 3 ln ∣ x ∣ + C

\int \frac{x ^{2} + 4 x}{( x + 2 ) ^{2}} d x

\int 2 x^{2} - 8 d x

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

\int \frac{x + \frac{1}{2}}{( x ^{2} - x + \frac{5}{4} )} d x

\int x 9 x^{2} - 1 d x

What is the integral of 2sqrt(x)-5^x+3/x ?
The integral of 2sqrt(x)-5^x+3/x is 4/3 x^{3/2}-(5^x)/(ln(5))+3ln|x|+C