(9) Compute R 1 √ 2−x2

Problem set 15: indefinite integrals I.

(1) Calculate R ₅

xdx.

(2) Compute R a^xdx for a > 0.

(3) Calculate R sin(x) cos(x) dx.

(4) Compute R sin(x)

1−cos(x)dx where it is defined.

(5) Compute R ₁

x log(log(log(x)))dx.

(6) Calculate R log(x) dx.

(7) Give R ₁

x²+2x+1dx.

(8) Compute R ₁

x²+2x+2dx.

(9) Compute R ₁

√ 2−x². (10) What is R ₁

√2+x² dx?

(11) Compute R x²√

3x³− 3 dx.

(12) Give R 3x²e^x3dx.

(13) Give the solution of R _log(x)

x dx.

(14) Compute R _x

√

1−x⁴ dx.

(15) Determine R e^xcos(x) dx.

(16) What is R x⁸log(x) dx.

(17) What is the primitive of log(x)²? (18) Compute R (x³−1)³

3x² dx.

(19) Derive R √a + bx dx.

(20) What is R _e^1/x

x² dx?

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