Question

indefinite integral of 2x+5/cube root of x

Answer 1

I got the answer when x>0 but i need the general answer

Answer 2

that could mean anything, have you tried drawing it ?!?!

🍀

Answer 3

we havent been taught how to draw it

Answer 4

scan it!

Answer 5

the picture is blank

Answer 6

scan it?

Answer 7

but in a way that your problem is clear :p

Answer 8

\[(2x+5)\div \sqrt[3]{x}\]

Answer 9

the indefinite integral of that

Answer 10

you are still using \(\div\) signs?!?! yet doing calculus?!?! that is funny 😀

maybe you mean \(\dfrac{(2x+5)}{ \sqrt[3]{x}}\)???

so break out the exponent rules, ..., and go from there.

cheers!

Answer 11

lets do an example:

\(\large\color{black}{\displaystyle\int\limits_{~}^{~}\frac{3x-6}{\sqrt[5]{x}}{\rm~d}x}\)

\(\large\color{black}{\displaystyle\sqrt[5]{x}=\sqrt[5]{x^1}=x^{1/5}}\)


\(\large\color{black}{\displaystyle\int\limits_{~}^{~}\frac{3x-6}{x^{1/5}}{\rm~d}x}\)

\(\large\color{black}{\displaystyle\int\limits_{~}^{~}\frac{3x}{x^{1/5}} - \frac{6}{x^{1/5}}{\rm~d}x}\)

\(\large\color{black}{\displaystyle\int\limits_{~}^{~}\frac{3x}{x^{1/5}}{\rm~d}x - \int\limits_{~}^{~}\frac{6}{x^{1/5}}{\rm~d}x}\)

\(\large\color{black}{\displaystyle 3x \div x^{1/5}=3x^1 \div x^{1/5}=3x^{1~-~1/5}=3x^{4/5}}\)

\(\large\color{black}{\displaystyle 6 \div x^{1/5}=6 \times x^{-1/5}=6 x^{-1/5}}\)

\(\large\color{black}{\displaystyle\int\limits_{~}^{~}3x^{4/5}{\rm~d}x - \int\limits_{~}^{~}6 x^{-1/5}{\rm~d}x}\)

\(\large\color{green}{\displaystyle \frac{1}{4/5~+1}\cdot 3\cdot x^{4/5~+1} {~~-~~} \frac{1}{-1/5~+1}\cdot6 \cdot x^{-1/5} }\)

\(\large\color{green}{\displaystyle \frac{1}{9/5}\cdot 3\cdot x^{9/5} {~~-~~} \frac{1}{4/5}\cdot6 \cdot x^{4/5}}\)

\(\large\color{green}{\displaystyle \frac{5}{9}\cdot 3\cdot x^{9/5} {~~-~~} \frac{5}{4}\cdot6 \cdot x^{4/5} }\)

\(\large\color{green}{\displaystyle \frac{5}{3} x^{9/5} {~~-~~} \frac{15}{2} x^{4/5} }\)

\(\large\color{red}{\displaystyle \frac{5}{3} x^{9/5} - \frac{15}{2} x^{4/5}+C }\)