Integration by Parts
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NEET DIGITAL LIBRARY
Integral Calculus

86335 If \(\int \frac{\sin 2 x}{\sin 5 x \sin 3 x} d x=\frac{1}{3} \log |\sin 3 x|-\frac{1}{5} \log |f(x)|+C\) then \(f(x)=\)

1 \(\sin 5 x\)
2 \(\sin 4 x\)
3 \(\sin 2 x\)
4 \(\sin 6 x\)
GUJCET-2017
Integral Calculus

86336 \(\int(2+\log x)(e x)^{x} d x=\) \(+\mathbf{C} ; \mathbf{x}>\mathbf{1}\)

1 \(x^{x}\)
2 \((e x)^{-x}\)
3 \((\mathrm{ex})^{\mathrm{x}}\)
4 \(e^{x^{x}}\)
GUJCET-2019
Integral Calculus

86337 If \(\int \sin ^{13} x \cos ^{3} x d x=A \sin ^{14} x+B \sin ^{16} x+C\), then \(\mathbf{A}+\mathbf{B}=\)

1 \(\frac{17}{112}\)
2 \(\frac{15}{112}\)
3 \(\frac{1}{110}\)
4 \(\frac{1}{112}\)
GUJCET-2019
Integral Calculus

86338 \(\int \frac{1}{\cos (x+4) \cos (x+2)} d x\) is equal to

1 \(\frac{1}{\sin 2} \log \left|\cos (\mathrm{x}+4)^{2}\right|+\mathrm{c}\)
2 \(\frac{1}{2} \log \left|\frac{\sec (\mathrm{x}+2)}{\sec (\mathrm{x}+4)}\right|+\mathrm{c}\)
3 \(\frac{1}{\sin 2} \log \left|\frac{\sec (x+4)}{\sec (x+2)}\right|+c\)
4 \(\log \left|\frac{\sec (\mathrm{x}+4)}{\sec (\mathrm{x}+2)}\right|+\mathrm{c}\)
TS EAMCET-2016
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Integral Calculus

86335 If \(\int \frac{\sin 2 x}{\sin 5 x \sin 3 x} d x=\frac{1}{3} \log |\sin 3 x|-\frac{1}{5} \log |f(x)|+C\) then \(f(x)=\)

1 \(\sin 5 x\)
2 \(\sin 4 x\)
3 \(\sin 2 x\)
4 \(\sin 6 x\)
GUJCET-2017
Integral Calculus

86336 \(\int(2+\log x)(e x)^{x} d x=\) \(+\mathbf{C} ; \mathbf{x}>\mathbf{1}\)

1 \(x^{x}\)
2 \((e x)^{-x}\)
3 \((\mathrm{ex})^{\mathrm{x}}\)
4 \(e^{x^{x}}\)
GUJCET-2019
Integral Calculus

86337 If \(\int \sin ^{13} x \cos ^{3} x d x=A \sin ^{14} x+B \sin ^{16} x+C\), then \(\mathbf{A}+\mathbf{B}=\)

1 \(\frac{17}{112}\)
2 \(\frac{15}{112}\)
3 \(\frac{1}{110}\)
4 \(\frac{1}{112}\)
GUJCET-2019
Integral Calculus

86338 \(\int \frac{1}{\cos (x+4) \cos (x+2)} d x\) is equal to

1 \(\frac{1}{\sin 2} \log \left|\cos (\mathrm{x}+4)^{2}\right|+\mathrm{c}\)
2 \(\frac{1}{2} \log \left|\frac{\sec (\mathrm{x}+2)}{\sec (\mathrm{x}+4)}\right|+\mathrm{c}\)
3 \(\frac{1}{\sin 2} \log \left|\frac{\sec (x+4)}{\sec (x+2)}\right|+c\)
4 \(\log \left|\frac{\sec (\mathrm{x}+4)}{\sec (\mathrm{x}+2)}\right|+\mathrm{c}\)
TS EAMCET-2016
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Integral Calculus

86335 If \(\int \frac{\sin 2 x}{\sin 5 x \sin 3 x} d x=\frac{1}{3} \log |\sin 3 x|-\frac{1}{5} \log |f(x)|+C\) then \(f(x)=\)

1 \(\sin 5 x\)
2 \(\sin 4 x\)
3 \(\sin 2 x\)
4 \(\sin 6 x\)
GUJCET-2017
Integral Calculus

86336 \(\int(2+\log x)(e x)^{x} d x=\) \(+\mathbf{C} ; \mathbf{x}>\mathbf{1}\)

1 \(x^{x}\)
2 \((e x)^{-x}\)
3 \((\mathrm{ex})^{\mathrm{x}}\)
4 \(e^{x^{x}}\)
GUJCET-2019
Integral Calculus

86337 If \(\int \sin ^{13} x \cos ^{3} x d x=A \sin ^{14} x+B \sin ^{16} x+C\), then \(\mathbf{A}+\mathbf{B}=\)

1 \(\frac{17}{112}\)
2 \(\frac{15}{112}\)
3 \(\frac{1}{110}\)
4 \(\frac{1}{112}\)
GUJCET-2019
Integral Calculus

86338 \(\int \frac{1}{\cos (x+4) \cos (x+2)} d x\) is equal to

1 \(\frac{1}{\sin 2} \log \left|\cos (\mathrm{x}+4)^{2}\right|+\mathrm{c}\)
2 \(\frac{1}{2} \log \left|\frac{\sec (\mathrm{x}+2)}{\sec (\mathrm{x}+4)}\right|+\mathrm{c}\)
3 \(\frac{1}{\sin 2} \log \left|\frac{\sec (x+4)}{\sec (x+2)}\right|+c\)
4 \(\log \left|\frac{\sec (\mathrm{x}+4)}{\sec (\mathrm{x}+2)}\right|+\mathrm{c}\)
TS EAMCET-2016
NEET DIGITAL LIBRARY
Integral Calculus

86335 If \(\int \frac{\sin 2 x}{\sin 5 x \sin 3 x} d x=\frac{1}{3} \log |\sin 3 x|-\frac{1}{5} \log |f(x)|+C\) then \(f(x)=\)

1 \(\sin 5 x\)
2 \(\sin 4 x\)
3 \(\sin 2 x\)
4 \(\sin 6 x\)
GUJCET-2017
Integral Calculus

86336 \(\int(2+\log x)(e x)^{x} d x=\) \(+\mathbf{C} ; \mathbf{x}>\mathbf{1}\)

1 \(x^{x}\)
2 \((e x)^{-x}\)
3 \((\mathrm{ex})^{\mathrm{x}}\)
4 \(e^{x^{x}}\)
GUJCET-2019
Integral Calculus

86337 If \(\int \sin ^{13} x \cos ^{3} x d x=A \sin ^{14} x+B \sin ^{16} x+C\), then \(\mathbf{A}+\mathbf{B}=\)

1 \(\frac{17}{112}\)
2 \(\frac{15}{112}\)
3 \(\frac{1}{110}\)
4 \(\frac{1}{112}\)
GUJCET-2019
Integral Calculus

86338 \(\int \frac{1}{\cos (x+4) \cos (x+2)} d x\) is equal to

1 \(\frac{1}{\sin 2} \log \left|\cos (\mathrm{x}+4)^{2}\right|+\mathrm{c}\)
2 \(\frac{1}{2} \log \left|\frac{\sec (\mathrm{x}+2)}{\sec (\mathrm{x}+4)}\right|+\mathrm{c}\)
3 \(\frac{1}{\sin 2} \log \left|\frac{\sec (x+4)}{\sec (x+2)}\right|+c\)
4 \(\log \left|\frac{\sec (\mathrm{x}+4)}{\sec (\mathrm{x}+2)}\right|+\mathrm{c}\)
TS EAMCET-2016
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