Integrate the following functions w.r.t. x: (2 x+1) x+2 - Vidyadip

Question

Integrate the following functions w.r.t. x:
$(2 x+1) \sqrt{x+2}$

✓

Answer

Let $I=\int(2 x+1) \sqrt{x+2} d x$Put $x+2=t \quad \therefore d x=d t$
Also, $x=t-2$
$ \therefore 2 x+1=2(t-2)+1=2 t-3$
$\therefore I=\int(2 t-3) \sqrt{t} d t$
$=\int\left(2 t^{\frac{3}{2}}-3 t^{\frac{1}{2}}\right) d t$
$=2 \int t^{\frac{3}{2}} d t-3 \int t^{\frac{1}{2}} d t$
$=2 \cdot \frac{t^{\frac{5}{2}}}{\left(\frac{5}{2}\right)}-3 \cdot \frac{t^{\frac{3}{2}}}{\left(\frac{3}{2}\right)}+c$
$=\frac{4}{5}(x+2)^{\frac{5}{2}}-2(x+2)^{\frac{3}{2}}+c$.

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 "Solve the Following Question.(2 Marks)" 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 $\vec{\text{a}},\vec{\text{b}}$ are two vectors, then write the truth value of the following statement:$\big|\vec{\text{a}}\big|=\big|\vec{\text{b}}\big|\Rightarrow\vec{\text{a}}=\vec{\text{b}}$

If $A=\left[\begin{array}{cc}2 & -2 \\ 4 & 3\end{array}\right]$ then find $A^{-1}$ by adjoint method.

If $\hat{\text{a}},\hat{\text{b}}$ are unit vectors such that $\hat{\text{a}}+\hat{\text{b}}$ is a unit vector, write the value of $\big|\hat{\text{a}}-\hat{\text{b}}\big|.$

Find matrices X and Y, if $\text{X}+\text{Y}=\begin{bmatrix}5&2\\0&9\end{bmatrix}$ and $\text{X}-\text{Y}=\begin{bmatrix}3&6\\0&-1\end{bmatrix}$

Evaluate :
$\underset{\overset{\int}{0}}{{\frac{\pi}{4}}} \sqrt{1+\sin 2 x} \cdot d x$

Using truth tables prove the following logical equivalences. [~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r

If $A=\{2,3,4,5,6\}$, then which of the following is 'not' true ?

Evaluate the following : $\int \frac{\cos x-\cos 2 x}{1-\cos x} \cdot d x$

If $\vec{\text{a}}=3\hat{\text{i}}-\hat{\text{j}}-4\hat{\text{k}},\ \vec{\text{b}}=-2\hat{\text{i}}+4\hat{\text{j}}-3\hat{\text{k}}$ and $\vec{\text{c}}=\hat{\text{i}}+2\hat{\text{j}}-\hat{\text{k}}$, find $|3\vec{\text{a}}-2\vec{\text{b}}+4\vec{\text{c}}|$.

A bag contains 8 marbles of which 3 are blue and 5 are red. One marble is drawn at random, its cooler is noted and the marble is replaced in the bag. A marble is again drawn from the bag and its colour is noted. Find the probability that the marble will be,
Blue and red in any order.