Leibnitz's Rules
Integral Calculus

86766 \(\int_{0}^{\pi / 2} \frac{\tan ^{7} x}{\cot ^{7} x+\tan ^{7} x} d x \text { is equal to }\)

1 \(\frac{\pi}{4}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{3}\)
Integral Calculus

86767 The value of \(\int_{-1}^{2} \frac{|x|}{x} d x\) is

1 0
2 1
3 2
4 3
Integral Calculus

86768 \(\int_{0}^{3} x(1-x)^{3 / 2} d x=\)

1 \(\frac{4}{35}\)
2 \(\frac{-2}{35}\)
3 \(\frac{-8}{35}\)
4 \(\frac{24}{35}\)
Integral Calculus

86773 \(\int \frac{1}{(x+1) \sqrt{x^{2}-1}} d x=\)

1 \(\sqrt{\frac{x+1}{x-1}}+C\)
2 \(\sqrt{\frac{x^{2}-1}{x+1}}+C\)
3 \(\sqrt{\frac{x-1}{x+1}}+C\)
4 \(\sqrt{\frac{x-1}{x^{2}+1}}+C\)
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Integral Calculus

86766 \(\int_{0}^{\pi / 2} \frac{\tan ^{7} x}{\cot ^{7} x+\tan ^{7} x} d x \text { is equal to }\)

1 \(\frac{\pi}{4}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{3}\)
Integral Calculus

86767 The value of \(\int_{-1}^{2} \frac{|x|}{x} d x\) is

1 0
2 1
3 2
4 3
Integral Calculus

86768 \(\int_{0}^{3} x(1-x)^{3 / 2} d x=\)

1 \(\frac{4}{35}\)
2 \(\frac{-2}{35}\)
3 \(\frac{-8}{35}\)
4 \(\frac{24}{35}\)
Integral Calculus

86773 \(\int \frac{1}{(x+1) \sqrt{x^{2}-1}} d x=\)

1 \(\sqrt{\frac{x+1}{x-1}}+C\)
2 \(\sqrt{\frac{x^{2}-1}{x+1}}+C\)
3 \(\sqrt{\frac{x-1}{x+1}}+C\)
4 \(\sqrt{\frac{x-1}{x^{2}+1}}+C\)
Integral Calculus

86766 \(\int_{0}^{\pi / 2} \frac{\tan ^{7} x}{\cot ^{7} x+\tan ^{7} x} d x \text { is equal to }\)

1 \(\frac{\pi}{4}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{3}\)
Integral Calculus

86767 The value of \(\int_{-1}^{2} \frac{|x|}{x} d x\) is

1 0
2 1
3 2
4 3
Integral Calculus

86768 \(\int_{0}^{3} x(1-x)^{3 / 2} d x=\)

1 \(\frac{4}{35}\)
2 \(\frac{-2}{35}\)
3 \(\frac{-8}{35}\)
4 \(\frac{24}{35}\)
Integral Calculus

86773 \(\int \frac{1}{(x+1) \sqrt{x^{2}-1}} d x=\)

1 \(\sqrt{\frac{x+1}{x-1}}+C\)
2 \(\sqrt{\frac{x^{2}-1}{x+1}}+C\)
3 \(\sqrt{\frac{x-1}{x+1}}+C\)
4 \(\sqrt{\frac{x-1}{x^{2}+1}}+C\)
Integral Calculus

86766 \(\int_{0}^{\pi / 2} \frac{\tan ^{7} x}{\cot ^{7} x+\tan ^{7} x} d x \text { is equal to }\)

1 \(\frac{\pi}{4}\)
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{6}\)
4 \(\frac{\pi}{3}\)
Integral Calculus

86767 The value of \(\int_{-1}^{2} \frac{|x|}{x} d x\) is

1 0
2 1
3 2
4 3
Integral Calculus

86768 \(\int_{0}^{3} x(1-x)^{3 / 2} d x=\)

1 \(\frac{4}{35}\)
2 \(\frac{-2}{35}\)
3 \(\frac{-8}{35}\)
4 \(\frac{24}{35}\)
Integral Calculus

86773 \(\int \frac{1}{(x+1) \sqrt{x^{2}-1}} d x=\)

1 \(\sqrt{\frac{x+1}{x-1}}+C\)
2 \(\sqrt{\frac{x^{2}-1}{x+1}}+C\)
3 \(\sqrt{\frac{x-1}{x+1}}+C\)
4 \(\sqrt{\frac{x-1}{x^{2}+1}}+C\)