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Integration by Parts
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Integration by Parts
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Qn #1564
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00:00
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If $ \int \frac{xe^{x}}{\sqrt{1+e^{x}}}=f(x)\sqrt{1+e^{x}}-2log \frac{\sqrt{1+e^{x}}-1}{\sqrt{1+e^{x}}+1}+C$ then $f(x)$ is
A.
$2x-1$
B.
$2x-4$
C.
$x+4$
D.
$x-1$
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Qn #1522
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The value of $\int \sqrt{x} e^{\sqrt{x}} dx$ is equal to:
A.
$$2\sqrt{x}-e^{\sqrt{x}-4\sqrt{xe^{\sqrt{x}}}}+C$$
B.
$$(2x-4\sqrt{x}+4)e^{\sqrt{x}}+C$$
C.
$$(2x+4\sqrt{x}+4)e^{\sqrt{x}}+C$$
D.
$$(1-4\sqrt{x})e^{\sqrt{x}}$$
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Qn #1430
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If $\int e^{x}(f(x)-f'(x))dx=\phi(x)$ , then the value of $\int e^x f(x) dx$ is
A.
$$\phi(x)+e^xf(x)$$
B.
$$\phi(x)-e^xf(x)$$
C.
$$\frac{1}{2}[e^xf(x)+\phi(x)]$$
D.
$$\frac{1}{2}[e^xf'(x)+\phi(x)]$$
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Qn #1272
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The value of $\int_{0}^{\pi}x^3 \sin x dx$
A.
π
3
-6π
B.
- π
3
- 6π
C.
- π
3
+ 6π
D.
π
3
+ 6π
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