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Integral Calculus

86252 \(\int_{-\pi / 4}^{\pi / 4} \frac{d x}{1+\cos 2 x}\) is equal to

1 1
2 2
3 3
4 4
COMEDK-2017
Integral Calculus

86253 The value of \(\int \frac{d x}{\sqrt{x}+\sqrt[3]{x}}\) is

1 \(3 \sqrt{x}+3(\sqrt[3]{x})-6 \sqrt[6]{x}+\log (\sqrt[6]{x}+1)+C\)
2 \(2 \sqrt{x}+6(\sqrt[6]{x})-6 \log (\sqrt[6]{x}+1)+C\)
3 \(2 \sqrt{x}-3(\sqrt[3]{x})+6(\sqrt[6]{x})-6 \log (\sqrt[6]{x}-1)+C\)
4 None of the above
COMEDK-2017
Integral Calculus

86255 If \(\int \frac{d x}{\left(x^{2}+1\right)\left(x^{2}+4\right)}=A \tan ^{-1} \frac{x}{2}+B \tan ^{-1} x+C\), Then \(A+B=\)

1 \(\frac{1}{2}\)
2 \(\frac{1}{3}\)
3 \(\frac{1}{4}\)
4 \(\frac{1}{6}\)
COMEDK-2018
Integral Calculus

86286 If \(f(x)\) is a polynomial of the second degree in a such that \(f(0)=f(1)=3, f(2)=-3\). Then, \(\int \frac{f(\mathrm{x})}{\mathrm{x}^{3}-1} \mathrm{dx}=\)

1 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{(\mathrm{x}-1)}\right)+\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
2 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{(\mathrm{x}-1)}\right)-\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
3 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{(\mathrm{x}-1)}\right)-\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
4 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{|\mathrm{x}-1|}\right)+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
AP EAMCET-2020-17.09.2020
NEET DIGITAL LIBRARY
Integral Calculus

86252 \(\int_{-\pi / 4}^{\pi / 4} \frac{d x}{1+\cos 2 x}\) is equal to

1 1
2 2
3 3
4 4
COMEDK-2017
Integral Calculus

86253 The value of \(\int \frac{d x}{\sqrt{x}+\sqrt[3]{x}}\) is

1 \(3 \sqrt{x}+3(\sqrt[3]{x})-6 \sqrt[6]{x}+\log (\sqrt[6]{x}+1)+C\)
2 \(2 \sqrt{x}+6(\sqrt[6]{x})-6 \log (\sqrt[6]{x}+1)+C\)
3 \(2 \sqrt{x}-3(\sqrt[3]{x})+6(\sqrt[6]{x})-6 \log (\sqrt[6]{x}-1)+C\)
4 None of the above
COMEDK-2017
Integral Calculus

86255 If \(\int \frac{d x}{\left(x^{2}+1\right)\left(x^{2}+4\right)}=A \tan ^{-1} \frac{x}{2}+B \tan ^{-1} x+C\), Then \(A+B=\)

1 \(\frac{1}{2}\)
2 \(\frac{1}{3}\)
3 \(\frac{1}{4}\)
4 \(\frac{1}{6}\)
COMEDK-2018
Integral Calculus

86286 If \(f(x)\) is a polynomial of the second degree in a such that \(f(0)=f(1)=3, f(2)=-3\). Then, \(\int \frac{f(\mathrm{x})}{\mathrm{x}^{3}-1} \mathrm{dx}=\)

1 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{(\mathrm{x}-1)}\right)+\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
2 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{(\mathrm{x}-1)}\right)-\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
3 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{(\mathrm{x}-1)}\right)-\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
4 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{|\mathrm{x}-1|}\right)+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
AP EAMCET-2020-17.09.2020
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Integral Calculus

86252 \(\int_{-\pi / 4}^{\pi / 4} \frac{d x}{1+\cos 2 x}\) is equal to

1 1
2 2
3 3
4 4
COMEDK-2017
Integral Calculus

86253 The value of \(\int \frac{d x}{\sqrt{x}+\sqrt[3]{x}}\) is

1 \(3 \sqrt{x}+3(\sqrt[3]{x})-6 \sqrt[6]{x}+\log (\sqrt[6]{x}+1)+C\)
2 \(2 \sqrt{x}+6(\sqrt[6]{x})-6 \log (\sqrt[6]{x}+1)+C\)
3 \(2 \sqrt{x}-3(\sqrt[3]{x})+6(\sqrt[6]{x})-6 \log (\sqrt[6]{x}-1)+C\)
4 None of the above
COMEDK-2017
Integral Calculus

86255 If \(\int \frac{d x}{\left(x^{2}+1\right)\left(x^{2}+4\right)}=A \tan ^{-1} \frac{x}{2}+B \tan ^{-1} x+C\), Then \(A+B=\)

1 \(\frac{1}{2}\)
2 \(\frac{1}{3}\)
3 \(\frac{1}{4}\)
4 \(\frac{1}{6}\)
COMEDK-2018
Integral Calculus

86286 If \(f(x)\) is a polynomial of the second degree in a such that \(f(0)=f(1)=3, f(2)=-3\). Then, \(\int \frac{f(\mathrm{x})}{\mathrm{x}^{3}-1} \mathrm{dx}=\)

1 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{(\mathrm{x}-1)}\right)+\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
2 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{(\mathrm{x}-1)}\right)-\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
3 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{(\mathrm{x}-1)}\right)-\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
4 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{|\mathrm{x}-1|}\right)+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
AP EAMCET-2020-17.09.2020
For More Updates join with Us
Integral Calculus

86252 \(\int_{-\pi / 4}^{\pi / 4} \frac{d x}{1+\cos 2 x}\) is equal to

1 1
2 2
3 3
4 4
COMEDK-2017
Integral Calculus

86253 The value of \(\int \frac{d x}{\sqrt{x}+\sqrt[3]{x}}\) is

1 \(3 \sqrt{x}+3(\sqrt[3]{x})-6 \sqrt[6]{x}+\log (\sqrt[6]{x}+1)+C\)
2 \(2 \sqrt{x}+6(\sqrt[6]{x})-6 \log (\sqrt[6]{x}+1)+C\)
3 \(2 \sqrt{x}-3(\sqrt[3]{x})+6(\sqrt[6]{x})-6 \log (\sqrt[6]{x}-1)+C\)
4 None of the above
COMEDK-2017
Integral Calculus

86255 If \(\int \frac{d x}{\left(x^{2}+1\right)\left(x^{2}+4\right)}=A \tan ^{-1} \frac{x}{2}+B \tan ^{-1} x+C\), Then \(A+B=\)

1 \(\frac{1}{2}\)
2 \(\frac{1}{3}\)
3 \(\frac{1}{4}\)
4 \(\frac{1}{6}\)
COMEDK-2018
Integral Calculus

86286 If \(f(x)\) is a polynomial of the second degree in a such that \(f(0)=f(1)=3, f(2)=-3\). Then, \(\int \frac{f(\mathrm{x})}{\mathrm{x}^{3}-1} \mathrm{dx}=\)

1 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{(\mathrm{x}-1)}\right)+\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
2 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{(\mathrm{x}-1)}\right)-\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
3 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{(\mathrm{x}-1)}\right)-\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
4 \(\log \left(\frac{\mathrm{x}^{2}+\mathrm{x}+1}{|\mathrm{x}-1|}\right)+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{3}}\right)+\mathrm{c}\)
AP EAMCET-2020-17.09.2020