Find the integral of 3x^2 + 4x + 9 with respect to x.

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We must first remember that to integrate, we must increase the power by 1 and divide by this new power.

Therefore, to integrate 3x^2 + 4x + 9, we take the first term, 3x^2. Using the above method, we find that the integral of this is (3x^3)/3 = x^3.

Taking the second term, 4x, we find the integral to be (4x^2)/2 = 2x^3.

Taking the final term, 9, we find the integral to be (9x)/1 = 9x.

As the question gives an indefinite integral (an integral without any limits) we must also remember to add a constant, which we can call C.

Therefore, the integral of 3x^2 + 4x + 9 with respect to x is 2x^2 + x^3 + 9x + C.

Dylan J. A Level Maths tutor, GCSE Maths tutor

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