Integrate the following functions w.r.t. x: 3 x^3-2 x+5 x x - Vidyadip

Question

Integrate the following functions w.r.t. x:
$\frac{3 x^3-2 x+5}{x \sqrt{x}}$

✓

Answer

$\int \frac{3 x^3-2 x+5}{x \sqrt{x}} d x$
$=\int x^{-\frac{3}{2}}\left(3 x^3-2 x+5\right) d x$
$=\int\left(3 x^{\frac{3}{2}}-2 x^{-\frac{1}{2}}+5 x^{-\frac{3}{2}}\right) d x$
$=3 \int x^{\frac{3}{2}} d x-2 \int x^{-\frac{1}{2}} d x+5 \int x^{-\frac{3}{2}} d x$
$=3\left(\frac{x^{\frac{3}{2}+1}}{\frac{3}{2}+1}\right)-2\left(\frac{x^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}\right)+5\left(\frac{x^{-\frac{3}{2}+1}}{-\frac{3}{2}+1}\right)+c$
$=\frac{6}{5} x^2 \sqrt{x}-4 \sqrt{x}-\frac{10}{\sqrt{x}}+c$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Answer the following questions in short." from Indefinite Integration→Indefinite Integration — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $X \sim B (n, p)$ and $n=10, E ( X )=5$, then find the value of $p$.

Find the separate equations of the lines represented by following equations: $3 y^2+7 x y=0$

Check the validity of the Rolle’s theorem for the following functions.

$f(x)=x^2-4 x+3, x \in[1,3]$

$\int \sqrt{x} \sec (x)^{\frac{3}{2}} \tan (x)^{\frac{3}{2}} d x$

A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received ₹ 2800 as interest. However, if trust had interchanged money in bonds, they would have got ₹ 100 less as interest. Using matrix method, find the amount invested by the trust.

The points $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ have position vectors $\bar{a}, \bar{b}$ and $\bar{c}$ respectively. The point $\mathrm{P}$ is

midpoint of $A B$. Find in terms of $\bar{a}, \bar{b}$ and $\bar{c}$ the vector $\overline{P C}$

Evaluate the following : $\int \cos ^3 x \cdot d x$

Find the general solution of $\sec ^2 2 \theta=1-\tan 2 \theta$

Find the principal solutions of cosec x = 2

Write the truth values of the following statements :
$\forall n \in N, n^2+n$ is even number while $n ^2- n$ is an odd number.