Integrate the function x^ 2 +4 x-5 - Vidyadip

Question

Integrate the function $\sqrt{x^{2}+4 x-5}$

✓

Answer

$I=\sqrt{x^{2}+4 x-5} d x$
= $\int \sqrt{\left(x^{2}+4 x+4\right)-9} d x$
= $\int \sqrt{(x+2)^{2}-(3)^{2}} d x$
We know that,
$\Rightarrow \int \sqrt{x^{2}-a^{2}} d x=\frac{x}{2} \sqrt{x^{2}-a^{2}}-\frac{a^{2}}{2} \log |x+\sqrt{x^{2}-a^{2}}|+C$
$\Rightarrow \mathrm{I}=\frac{(\mathrm{x}+2)}{2} \sqrt{\mathrm{x}^{2}+4 \mathrm{x}-5}-\frac{9}{2} \log |(\mathrm{x}+2)+\sqrt{\mathrm{x}^{2}+4 \mathrm{x}-5}|+\mathrm{C}$

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 "3 Marks" from Integrals→Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the equation of the plane passing through the following points:
(2, 1, 0), (3, -2, -2) and (3, 1, 7)

Evaluate the following:
$\tan^{-1}\Big(-\frac{1}{\sqrt3}\Big)+\tan^{-1}\Big(-\sqrt3\Big)+\tan^{-1}\Big(\sin\Big(-\frac{\pi}{2}\Big)\Big)$

Find $|\vec{\text{a}|}$ and $\big|\vec{\text{b}}\big|$ if
$\big(\vec{\text{a}}+\vec{\text{b}}\big).\big(\vec{\text{a}}-\vec{\text{b}}\big)=3$ and $|\vec{\text{a}}|=2\big|\vec{\text{b}}\big|$

Evaluate the following integrals:
$\int_{\pi}^\limits{\frac{3\pi}{2}}\sqrt{1-\cos2\text{x}}\text{ dx}$

For each of the differential equations in find the general solution:
$\frac{\text{dy}}{\text{dx}}=\text{sin}^{-1}\text{x}$

If the function f: R$\rightarrow$R be given by f(x) = x² + 2 and g: R$\rightarrow$R be given by g(x) $ = \frac{\text{x}}{\text{x} - 1 },\text{x}\neq1 ,$ find fog and gof and hence find fog (2) and gof (–3).

Let $\text{A}=\begin{bmatrix}2&-3\\-7&5\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&0\\2&-4\end{bmatrix},$ verify that
$(\text{A}+\text{B})^\text{T}=\text{A}^\text{T}+\text{B}^\text{T}$

Let $\text{A}=\begin{bmatrix}-1&0&2\\3&1&4 \end{bmatrix},\text{ B}=\begin{bmatrix}0&-2&5\\1&-3&1 \end{bmatrix}$ and $\text{C}=\begin{bmatrix}1&-5&2\\6&0&-4 \end{bmatrix}.$ Compute 2A - 3B + 4C.

For the principal values, evaluate the following:
$\sin^{-1}\Big(-\frac{1}{2}\Big)+2\cos^{-1}\Big(-\frac{\sqrt3}{2}\Big)$

Show that the tangents to the curve y = 7x³ + 11 at the points x = 2 and x = -2 are parallel.