Find out the answer to "Determine the following indefinite integral. ∫(x34+x5)dx"

High School
Other

Adela Brown

Answered question

2021-12-31

Determine the following indefinite integral.
$\int (\sqrt[4]{x^{3}} + \sqrt{x^{5}}) d x$

Answer & Explanation

Cheryl King

Beginner2022-01-01Added 36 answers

Step 1
To evaluate the indefinite integral, $\int (\sqrt[4]{x^{3}} + \sqrt{x^{5}}) d x$ .
Solution:
The given integral is,
$\int (\sqrt[4]{x^{3}} + \sqrt{x^{5}}) d x$
Simplifying the given integral gives,
$\int (\sqrt[4]{x^{3}} + \sqrt{x^{5}}) d x = \int (x^{3 / 4} + x^{5 / 2}) d x$
$= \int x^{\frac{3}{4}} d x + \int x^{\frac{5}{2}} d x$
Step 2
Solving the given integral further we get,
$\int x^{\frac{3}{4}} d x + \int x^{\frac{5}{2}} d x = \frac{x^{\frac{7}{4}}}{\frac{7}{4}} + \frac{x^{\frac{7}{2}}}{\frac{7}{2}} + c$
$= \frac{4}{7} x^{\frac{7}{4}} + \frac{2}{7} x^{\frac{7}{2}} + c$
Hence, the value of the integral is $\frac{4}{7} x^{74} + 27 x^{72} + c$ .

Terry Ray

Beginner2022-01-02Added 50 answers

$\int (\sqrt{x^{5}} + \sqrt[4]{x^{3}}) d x$
$\int (x^{\frac{5}{2}} + x^{\frac{3}{4}}) d x$
$= \int x^{\frac{5}{2}} d x + \int x^{\frac{3}{4}} d x$
$\int x^{\frac{5}{2}} d x$
$= \frac{2 x^{\frac{7}{2}}}{7}$
$\int x^{\frac{3}{4}} d x$
$= \frac{4 x^{\frac{7}{4}}}{7}$
$\int x^{\frac{5}{2}} d x + \int x^{\frac{3}{4}} d x$
$= \frac{2 x^{\frac{7}{2}}}{7} + \frac{4 x^{\frac{7}{4}}}{7}$
$\int (x^{\frac{5}{2}} + x^{\frac{3}{4}}) d x$
$= \frac{2 x^{\frac{7}{2}}}{7} + \frac{4 x^{\frac{7}{4}}}{7} + C$
Let's rewrite / simplify:
$= \frac{2 (x^{\frac{7}{2}} + 2 x^{\frac{7}{4}})}{7} + C$

karton

Expert2022-01-04Added 613 answers

$\begin{matrix} \int \sqrt[4]{x^{3}} + \sqrt{x^{5}} d x \\ \int x^{\frac{3}{4}} + x^{2} \sqrt{x} d x \\ \int x^{\frac{3}{4}} + x^{2} \times x^{\frac{1}{2}} d x \\ \int x^{\frac{3}{4}} + x^{\frac{5}{2}} d x \\ \int x^{\frac{3}{4}} d x + \int x^{\frac{5}{2}} d x \\ \frac{4 x \sqrt[4]{x^{3}}}{7} + \frac{2 x^{3} \sqrt{x}}{7} \\ \frac{4 x \sqrt[4]{x^{3}} + 2 x^{3} \sqrt{x}}{7} \\ \frac{4 x \sqrt[4]{x^{3}} + 2 x^{3} \sqrt{x}}{7} + C \end{matrix}$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Other

Didn't find what you were looking for?