TS EAMCET · Maths · Indefinite Integration
\(\int\left(\frac{\left(\sin ^4 x+2 \cos ^2 x-1\right) \cos x}{(1+\sin x)^6}\right) d x=\)
- A \(\frac{\sin ^6 x}{6(1+\sin x)^6}+c\)
- B \(-\frac{\sin ^6 x}{6(1+\sin x)^6}+c\)
- C \(\frac{\cos ^6 x}{6(1+\sin x)^6}+c\)
- D \(-\frac{\cos ^6 x}{6(1+\sin x)^6}+c\)
Answer & Solution
Correct Answer
(D) \(-\frac{\cos ^6 x}{6(1+\sin x)^6}+c\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } I=\int \frac{\left(\sin ^4 x+2 \cos ^2 x-1\right)}{(1+\sin x)^6} \cos x d x \\ & =\int \frac{\left(\sin ^4 x-2 \sin ^2 x+1\right)}{(1+\sin x)^6} \cos x d x \\ & =\int \frac{\left(1-\sin ^2 x\right)^2}{(1+\sin x)^6} \cos x d x=\int \frac{(1-\sin…
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 angle between the tangents drawn from the point \(\mathrm{P}(\mathrm{k}, 6 \mathrm{k})\) to the circle \(x^2+y^2+6 x-6 y+2=0\) is \(2 \operatorname{Tan}^{-1}\left(\frac{4}{3}\right)\). If the coordinates of P are integers, then \(\mathrm{k}=\)TS EAMCET 2025 Medium
- In triangle ABC , if \(A=45^{\circ}, C=75^{\circ}\) and \(R=\sqrt{2}\), then \(r=\)TS EAMCET 2024 Medium
- The set of all values of \(x\) which satisfy both the inequations \(x^2-1 \leq 0\) and \(x^2-x-2 \geq 0\) simultaneously isTS EAMCET 2023 Medium
- If \(x=\cos ^3 \theta-\sin ^3 \theta\) and \(y=\sqrt[3]{\cos \theta}-\sqrt[3]{\sin \theta}\), then the the value of \(\frac{d y}{d x}\) at \(\theta=\frac{\pi}{4}\) isTS EAMCET 2023 Medium
- If \(\left[\begin{array}{ccc}-1 & 2 & b \\ a & 5 & 6 \\ 3 & c & 7\end{array}\right]\) is a symmetric matrix, then \(\left[\begin{array}{ccc}a & b & c \\ b & c & a \\ c & a & b\end{array}\right]=\)TS EAMCET 2022 Hard
- If \(f(x)=\int_x^{x+1} e^{-t^2} d t\), then the interval in which \(f(x)\) is decreasing isTS EAMCET 2019 Medium
More PYQs from TS EAMCET
- If lie outside thenTS EAMCET 2021 Easy
- The volume of water required to dissolve \(0.1 \mathrm{~g} \mathrm{PbCl}_2\) to get a saturated solution (in mL ) is \(\left(\right.\) Given \(\mathrm{K}_{\mathrm{sp}}\left(\mathrm{PbCl}_2\right)=3.2 \times 10^{-8} ;\) Atomic mass of \(\left.\mathrm{Pb}=207 \mathrm{u}\right)\)TS EAMCET 2025 Easy
- Which one of the following is not an iso-electronic pair?TS EAMCET 2002 Easy
- If \(\cos ^{-1}\left(\frac{y}{b}\right)=2 \log \left(\frac{x}{2}\right)\), where \(x>0\), then \(x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}\) is equal toTS EAMCET 2013 Medium
- If the displacement of a body is given by \(x=3 \cos \left[2 \pi t+\frac{\pi}{4}\right] \mathrm{m}\), then the acceleration of the body at \(t=2 \mathrm{~s}\) isTS EAMCET 2019 Easy
- A plane meets the coordinate axes at \(A, B, C\) so that the centroid of the triangle \(A B C\) is \((1,2,4)\). Then, the equation of the plane isTS EAMCET 2010 Medium