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10 questions
∫5sinxdx=\int_{ }^{ }5\sin xdx=∫5sinxdx=
-5sinx+c
-cosx+c
-5cosx+c
-cos5x+c
∫5sin5xdx=\int_{ }^{ }5\sin5xdx=∫5sin5xdx=
cos5x+c
-5cos5x+c
sin5x+c
∫6xdx=\int_{ }^{ }6^xdx=∫6xdx=
6xln6+c\frac{6^x}{\ln6}+cln66x+c
6x+c6^x+c6x+c
6xln6+c6^x\ln6+c6xln6+c
61+x1+x+c\frac{6^{1+x}}{1+x}+c1+x61+x+c
∫(x7+12x)dx=\int\left(x^7+\frac{1}{2\sqrt{x}}\right)dx=∫(x7+2x1)dx=
x7+12xx^7+\frac{1}{2\sqrt{x}}x7+2x1 +C
x88+x\frac{x^8}{8}+\sqrt{x}8x8+x +C
x8+12xx^8+\frac{1}{2\sqrt{x}}x8+2x1 +C
x88+2x\frac{x^8}{8}+2\sqrt{x}8x8+2x +C
∫(4x−7x+8ex)dx=\int\left(\frac{4}{\sqrt{x}}-\frac{7}{x}+8e^x\right)dx=∫(x4−x7+8ex)dx=
4x−7x+8ex\frac{4}{\sqrt{x}}-\frac{7}{x}+8e^xx4−x7+8ex +C
4x−7ln∣x∣+8ex4\sqrt{x}-7\ln\left|x\right|+8e^x4x−7ln∣x∣+8ex +C
8x−7ln∣x∣+8ex8\sqrt{x}-7\ln\left|x\right|+8e^x8x−7ln∣x∣+8ex +C
8x−7xln∣x∣+8xex8\sqrt{x}-7x\ln\left|x\right|+8xe^x8x−7xln∣x∣+8xex +C
∫(9x8+7)dx=\int\left(9x^8+7\right)dx=∫(9x8+7)dx=
9x8+79x^8+79x8+7
9x8+7+c9x^8+7+c9x8+7+c
9x8+7x+c9x^8+7x+c9x8+7x+c
x9+7x+cx^9+7x+cx9+7x+c
∫2cos8xdx=\int2\cos8xdx=∫2cos8xdx=
sin8x8+c\frac{\sin8x}{8}+c8sin8x+c
sin8x4+c\frac{\sin8x}{4}+c4sin8x+c
4sin8x+c
8sinx+c
∫10cos(5x−π4)dx=\int10\cos\left(5x-\frac{\pi}{4}\right)dx=∫10cos(5x−4π)dx=
2sin(5x−π4)+c2\sin\left(5x-\frac{\pi}{4}\right)+c2sin(5x−4π)+c
10sin(5x−π4)+c10\sin\left(5x-\frac{\pi}{4}\right)+c10sin(5x−4π)+c
10sinx+c
5cos(5x−π4)+c5\cos\left(5x-\frac{\pi}{4}\right)+c5cos(5x−4π)+c
∫(3x+5)4dx=\int\left(3x+5\right)^4dx=∫(3x+5)4dx=
(3x+5)44+c\frac{\left(3x+5\right)^4}{4}+c4(3x+5)4+c
(3x+5)515+c\frac{\left(3x+5\right)^5}{15}+c15(3x+5)5+c
(3x+5)412+c\frac{\left(3x+5\right)^4}{12}+c12(3x+5)4+c
4(3x+5)3+c4\left(3x+5\right)^3+c4(3x+5)3+c
∫2sin2(2x+π4)dx\int\frac{2}{\sin^2\left(2x+\frac{\pi}{4}\right)}dx∫sin2(2x+4π)2dx
−ctg(2x+π4)+c-\operatorname{ctg}\left(2x+\frac{\pi}{4}\right)+c−ctg(2x+4π)+c
ctg(2x+π4)+c\operatorname{ctg}\left(2x+\frac{\pi}{4}\right)+cctg(2x+4π)+c
−2ctg(2x+π4)+c-2\operatorname{ctg}\left(2x+\frac{\pi}{4}\right)+c−2ctg(2x+4π)+c
4ctg(2x+π4)+c4\operatorname{ctg}\left(2x+\frac{\pi}{4}\right)+c4ctg(2x+4π)+c
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