AP EAMCET · Maths · Indefinite Integration
\(\int e^x\left(\frac{x+2}{x+4}\right)^2 d x=\)
- A \(-\frac{x e^x}{(x+4)^2}+c\)
- B \(-\frac{x e^x}{(x+4)}+c\)
- C \(\frac{x e^x}{(x+4)}+c\)
- D \(\frac{2 x e^x}{(x+4)}+c\)
Answer & Solution
Correct Answer
(C) \(\frac{x e^x}{(x+4)}+c\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } \mathrm{I}=\int\left(\frac{x+2}{x+4}\right)^2 e^x d x=\int e^x\left[\frac{x^2+4+4 x}{(x+4)^2}\right] d x \\ & \Rightarrow \mathrm{I}=\int \frac{e^x x}{(x+4)} d x+\int \frac{4 e^x}{(x+4)^2} d x \end{aligned}\) Integrating by parts…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The general solution of the differential equation \(x d y-y d x=\sqrt{x^2+y^2} d x\) isAP EAMCET 2024 Medium
- A number is selected at random from the set \(\{1,2,3,4, \ldots, 1000\}\), then the probability of getting a number which is a perfect cube or a natural having odd number of divisors isAP EAMCET 2020 Easy
- \(E_1: a+b+c=0, \quad\) if 1 is a root of \(a x^2+b x+c=0, \quad E_2: b^2-a^2=2 a c\), if \(\sin \theta\), \(\cos \theta\) are the roots of \(a x^2+b x+c=0\) Which of the following is true?AP EAMCET 2005 Medium
- Let a triangle be inscribed in a circle of radius units. If the bisectors of the angles and are extended to cut the circle at and respectively, then the value ofAP EAMCET 2019 Medium
- If a complex number \(z=x+i y\) represents a point \(P\) on the Argand plane and \(\operatorname{Arg}\left(\frac{z-3+2 i}{z+2-3 i}\right)=\frac{\pi}{4}\), then the locus of \(P\) is aAP EAMCET 2025 Medium
- If \(\int \frac{\sin ^3 x\left(\tan ^{-1}(\sec x+\cos x)\right)^{-1}}{\left(\cos ^4 x+3 \cos ^2 x+1\right)} d x=f(x)+C\), then \(e^{\mathrm{f}(x)}=\)AP EAMCET 2022 Hard
More PYQs from AP EAMCET
- For \(a, b, h>0\), if the slope of one of the lines represented by \(a^2 x^2+2 h x y+b^2 y^2=0\) is twice that of the other, then the value of \(\frac{h}{a b}\) isAP EAMCET 2022 Hard
- \(P\) is a variable point such that the distance of \(P\) from \(A(4,0)\) is twice the distance of \(P\) from \(B(-4,0)\). If the line \(3 y-3 x-20=0\) intersects the locus of P at the points C and D , then the distance between C and D isAP EAMCET 2024 Easy
- Which of the following statements regarding adsorption theory of heterogeneous catalysis is not correct?AP EAMCET 2025 Easy
- Assertion (A) : It is more difficult to push a magnet into a coil with more number of turns.
Reason (R) : The emf induced in a coil opposes the motion of a magnet when it is moved towards the coil.AP EAMCET 2017 Easy - If \(P=(2,-3,4), Q=(-1,-4,0), R=(2,1,0)\) are three points and \(S\) is the foot of the perpendicular drawn from \(\mathrm{R}\) to \(\mathrm{PQ}\), then the \(\mathrm{X}\)-coordinate of \(\mathrm{S}\) isAP EAMCET 2018 Medium
- If the direction cosines of two lines are and , then identify the direction ratios of a line which is bisecting one of the angle between them.AP EAMCET 2021 Easy