Integration by Parts
« Previous Topic: Integrations and Integration of Functions Next Topic: Definite Integral as Limit of a Sum »
Integral Calculus

86342 If \(\left.\int \frac{9 x+15}{x^{2}-6 x-9} d x=\operatorname{Alog} \right\rvert\, g(x)\)
\(+B \log |\mathbf{f}(\mathbf{x})|+C \text {, then } \frac{(A-B) g(4)}{\mathbf{f}(-1)}=\)

1 3
2 \(\frac{1}{7}\)
3 1
4 \(\frac{3}{7}\)
TS EAMCET-2020-10.09.2020
Integral Calculus

86343 If \(\int x^{3}(\log x)^{2} d x=x^{4}\left[A(\log x)^{2}+B(\log x)\right.\) \(+C \log \mathbf{e}]+K\), then \(A+B+C\)

1 \(\frac{7}{24}\)
2 \(\frac{4}{25}\)
3 \(\frac{3}{14}\)
4 \(\frac{5}{32}\)
COMEDK-2016
Integral Calculus

86344 \(\int(x-a)\left(x^{n-1}+x^{n-2} a+\ldots \ldots .+a^{n-1}\right) d x=\)
(where \(\mathbf{C}\) is a constant of integration.)

1 \(\mathrm{na}^{\mathrm{n}-1}+\mathrm{C}\)
2 \(\frac{\mathrm{x}^{\mathrm{n}+1}}{\mathrm{n}+1}-\mathrm{a}^{\mathrm{n}}+\mathrm{C}\)
3 \(\mathrm{x}^{\mathrm{n}}-\mathrm{a}^{\mathrm{n}}+\mathrm{C}\)
4 \(\frac{x^{n+1}}{n+1}-a^{n} x+C\)
MHT CET-2022
Integral Calculus

86345 If \(f(x)=\int \frac{x^{2}+\sin ^{2} x}{1+x^{2}} \cdot \sec ^{2} x d x\) and \(f(0)=0\), then \((1)=\)

1 \(\frac{\pi}{4}-1\)
2 \(\tan 1+\frac{\pi}{4}\)
3 \(1-\frac{\pi}{4}\)
4 \(\tan 1-\frac{\pi}{4}\)
MHT CET-2022
Integral Calculus

86356 If \(\int \frac{\sin x}{\operatorname{six}(x-\alpha)} d x=A x+B \log \sin (x-\alpha)+C\),
then the value of \(A-B\) at \(\alpha=\frac{\pi}{2}\) is

1 -1
2 1
3 2
4 0
5 -2
Kerala CEE-2008
NEET DIGITAL LIBRARY
Integral Calculus

86342 If \(\left.\int \frac{9 x+15}{x^{2}-6 x-9} d x=\operatorname{Alog} \right\rvert\, g(x)\)
\(+B \log |\mathbf{f}(\mathbf{x})|+C \text {, then } \frac{(A-B) g(4)}{\mathbf{f}(-1)}=\)

1 3
2 \(\frac{1}{7}\)
3 1
4 \(\frac{3}{7}\)
TS EAMCET-2020-10.09.2020
Integral Calculus

86343 If \(\int x^{3}(\log x)^{2} d x=x^{4}\left[A(\log x)^{2}+B(\log x)\right.\) \(+C \log \mathbf{e}]+K\), then \(A+B+C\)

1 \(\frac{7}{24}\)
2 \(\frac{4}{25}\)
3 \(\frac{3}{14}\)
4 \(\frac{5}{32}\)
COMEDK-2016
Integral Calculus

86344 \(\int(x-a)\left(x^{n-1}+x^{n-2} a+\ldots \ldots .+a^{n-1}\right) d x=\)
(where \(\mathbf{C}\) is a constant of integration.)

1 \(\mathrm{na}^{\mathrm{n}-1}+\mathrm{C}\)
2 \(\frac{\mathrm{x}^{\mathrm{n}+1}}{\mathrm{n}+1}-\mathrm{a}^{\mathrm{n}}+\mathrm{C}\)
3 \(\mathrm{x}^{\mathrm{n}}-\mathrm{a}^{\mathrm{n}}+\mathrm{C}\)
4 \(\frac{x^{n+1}}{n+1}-a^{n} x+C\)
MHT CET-2022
Integral Calculus

86345 If \(f(x)=\int \frac{x^{2}+\sin ^{2} x}{1+x^{2}} \cdot \sec ^{2} x d x\) and \(f(0)=0\), then \((1)=\)

1 \(\frac{\pi}{4}-1\)
2 \(\tan 1+\frac{\pi}{4}\)
3 \(1-\frac{\pi}{4}\)
4 \(\tan 1-\frac{\pi}{4}\)
MHT CET-2022
Integral Calculus

86356 If \(\int \frac{\sin x}{\operatorname{six}(x-\alpha)} d x=A x+B \log \sin (x-\alpha)+C\),
then the value of \(A-B\) at \(\alpha=\frac{\pi}{2}\) is

1 -1
2 1
3 2
4 0
5 -2
Kerala CEE-2008
Join With Us for More Updates
Integral Calculus

86342 If \(\left.\int \frac{9 x+15}{x^{2}-6 x-9} d x=\operatorname{Alog} \right\rvert\, g(x)\)
\(+B \log |\mathbf{f}(\mathbf{x})|+C \text {, then } \frac{(A-B) g(4)}{\mathbf{f}(-1)}=\)

1 3
2 \(\frac{1}{7}\)
3 1
4 \(\frac{3}{7}\)
TS EAMCET-2020-10.09.2020
Integral Calculus

86343 If \(\int x^{3}(\log x)^{2} d x=x^{4}\left[A(\log x)^{2}+B(\log x)\right.\) \(+C \log \mathbf{e}]+K\), then \(A+B+C\)

1 \(\frac{7}{24}\)
2 \(\frac{4}{25}\)
3 \(\frac{3}{14}\)
4 \(\frac{5}{32}\)
COMEDK-2016
Integral Calculus

86344 \(\int(x-a)\left(x^{n-1}+x^{n-2} a+\ldots \ldots .+a^{n-1}\right) d x=\)
(where \(\mathbf{C}\) is a constant of integration.)

1 \(\mathrm{na}^{\mathrm{n}-1}+\mathrm{C}\)
2 \(\frac{\mathrm{x}^{\mathrm{n}+1}}{\mathrm{n}+1}-\mathrm{a}^{\mathrm{n}}+\mathrm{C}\)
3 \(\mathrm{x}^{\mathrm{n}}-\mathrm{a}^{\mathrm{n}}+\mathrm{C}\)
4 \(\frac{x^{n+1}}{n+1}-a^{n} x+C\)
MHT CET-2022
Integral Calculus

86345 If \(f(x)=\int \frac{x^{2}+\sin ^{2} x}{1+x^{2}} \cdot \sec ^{2} x d x\) and \(f(0)=0\), then \((1)=\)

1 \(\frac{\pi}{4}-1\)
2 \(\tan 1+\frac{\pi}{4}\)
3 \(1-\frac{\pi}{4}\)
4 \(\tan 1-\frac{\pi}{4}\)
MHT CET-2022
Integral Calculus

86356 If \(\int \frac{\sin x}{\operatorname{six}(x-\alpha)} d x=A x+B \log \sin (x-\alpha)+C\),
then the value of \(A-B\) at \(\alpha=\frac{\pi}{2}\) is

1 -1
2 1
3 2
4 0
5 -2
Kerala CEE-2008
For More Updates join with Us
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Integral Calculus

86342 If \(\left.\int \frac{9 x+15}{x^{2}-6 x-9} d x=\operatorname{Alog} \right\rvert\, g(x)\)
\(+B \log |\mathbf{f}(\mathbf{x})|+C \text {, then } \frac{(A-B) g(4)}{\mathbf{f}(-1)}=\)

1 3
2 \(\frac{1}{7}\)
3 1
4 \(\frac{3}{7}\)
TS EAMCET-2020-10.09.2020
Integral Calculus

86343 If \(\int x^{3}(\log x)^{2} d x=x^{4}\left[A(\log x)^{2}+B(\log x)\right.\) \(+C \log \mathbf{e}]+K\), then \(A+B+C\)

1 \(\frac{7}{24}\)
2 \(\frac{4}{25}\)
3 \(\frac{3}{14}\)
4 \(\frac{5}{32}\)
COMEDK-2016
Integral Calculus

86344 \(\int(x-a)\left(x^{n-1}+x^{n-2} a+\ldots \ldots .+a^{n-1}\right) d x=\)
(where \(\mathbf{C}\) is a constant of integration.)

1 \(\mathrm{na}^{\mathrm{n}-1}+\mathrm{C}\)
2 \(\frac{\mathrm{x}^{\mathrm{n}+1}}{\mathrm{n}+1}-\mathrm{a}^{\mathrm{n}}+\mathrm{C}\)
3 \(\mathrm{x}^{\mathrm{n}}-\mathrm{a}^{\mathrm{n}}+\mathrm{C}\)
4 \(\frac{x^{n+1}}{n+1}-a^{n} x+C\)
MHT CET-2022
Integral Calculus

86345 If \(f(x)=\int \frac{x^{2}+\sin ^{2} x}{1+x^{2}} \cdot \sec ^{2} x d x\) and \(f(0)=0\), then \((1)=\)

1 \(\frac{\pi}{4}-1\)
2 \(\tan 1+\frac{\pi}{4}\)
3 \(1-\frac{\pi}{4}\)
4 \(\tan 1-\frac{\pi}{4}\)
MHT CET-2022
Integral Calculus

86356 If \(\int \frac{\sin x}{\operatorname{six}(x-\alpha)} d x=A x+B \log \sin (x-\alpha)+C\),
then the value of \(A-B\) at \(\alpha=\frac{\pi}{2}\) is

1 -1
2 1
3 2
4 0
5 -2
Kerala CEE-2008
NEET DIGITAL LIBRARY
Integral Calculus

86342 If \(\left.\int \frac{9 x+15}{x^{2}-6 x-9} d x=\operatorname{Alog} \right\rvert\, g(x)\)
\(+B \log |\mathbf{f}(\mathbf{x})|+C \text {, then } \frac{(A-B) g(4)}{\mathbf{f}(-1)}=\)

1 3
2 \(\frac{1}{7}\)
3 1
4 \(\frac{3}{7}\)
TS EAMCET-2020-10.09.2020
Integral Calculus

86343 If \(\int x^{3}(\log x)^{2} d x=x^{4}\left[A(\log x)^{2}+B(\log x)\right.\) \(+C \log \mathbf{e}]+K\), then \(A+B+C\)

1 \(\frac{7}{24}\)
2 \(\frac{4}{25}\)
3 \(\frac{3}{14}\)
4 \(\frac{5}{32}\)
COMEDK-2016
Integral Calculus

86344 \(\int(x-a)\left(x^{n-1}+x^{n-2} a+\ldots \ldots .+a^{n-1}\right) d x=\)
(where \(\mathbf{C}\) is a constant of integration.)

1 \(\mathrm{na}^{\mathrm{n}-1}+\mathrm{C}\)
2 \(\frac{\mathrm{x}^{\mathrm{n}+1}}{\mathrm{n}+1}-\mathrm{a}^{\mathrm{n}}+\mathrm{C}\)
3 \(\mathrm{x}^{\mathrm{n}}-\mathrm{a}^{\mathrm{n}}+\mathrm{C}\)
4 \(\frac{x^{n+1}}{n+1}-a^{n} x+C\)
MHT CET-2022
Integral Calculus

86345 If \(f(x)=\int \frac{x^{2}+\sin ^{2} x}{1+x^{2}} \cdot \sec ^{2} x d x\) and \(f(0)=0\), then \((1)=\)

1 \(\frac{\pi}{4}-1\)
2 \(\tan 1+\frac{\pi}{4}\)
3 \(1-\frac{\pi}{4}\)
4 \(\tan 1-\frac{\pi}{4}\)
MHT CET-2022
Integral Calculus

86356 If \(\int \frac{\sin x}{\operatorname{six}(x-\alpha)} d x=A x+B \log \sin (x-\alpha)+C\),
then the value of \(A-B\) at \(\alpha=\frac{\pi}{2}\) is

1 -1
2 1
3 2
4 0
5 -2
Kerala CEE-2008